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All questions of Simultaneous Equations for Class 10 Exam
What is the general approach to solving a problem that requires finding ages based on given ratios?- a) Calculate averages
- b) Use proportions
- c) Guess and check
- d) Set up equations based on defined variables
Correct answer is option 'D'. Can you explain this answer?
What is the general approach to solving a problem that requires finding ages based on given ratios?
a)
Calculate averages
b)
Use proportions
c)
Guess and check
d)
Set up equations based on defined variables
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Foothill Academy answered |
The general approach to finding ages based on ratios is to set up equations using defined variables for each person's age. This systematic method allows for accurate solutions based on the relationships provided in the problem.
What is the primary method used to solve equations that can be transformed into linear equations due to variables in denominators?- a) Cross-multiplication
- b) Substitution
- c) Reduction
- d) Variable substitution
Correct answer is option 'D'. Can you explain this answer?
What is the primary method used to solve equations that can be transformed into linear equations due to variables in denominators?
a)
Cross-multiplication
b)
Substitution
c)
Reduction
d)
Variable substitution
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Foothill Academy answered |
The primary method for solving equations that have variables in the denominators involves variable substitution, such as letting \( 1/x = a \) or \( 1/y = b \). This transformation simplifies the problem into a linear format, making it easier to resolve.
How can you find two numbers based on their sum and difference?- a) Use multiplication
- b) Guess and check
- c) Set up two equations
- d) Visual representation
Correct answer is option 'C'. Can you explain this answer?
How can you find two numbers based on their sum and difference?
a)
Use multiplication
b)
Guess and check
c)
Set up two equations
d)
Visual representation
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Foothill Academy answered |
To find two numbers based on their sum and difference, you set up two equations: one for their sum and another for their difference. Solving this system provides the values of both numbers effectively.
In solving simultaneous linear equations using the substitution method, what is the first step?- a) Substitute the values of both variables
- b) Express one variable in terms of the other
- c) Add the equations together
- d) Multiply the equations by a common factor
Correct answer is option 'B'. Can you explain this answer?
In solving simultaneous linear equations using the substitution method, what is the first step?
a)
Substitute the values of both variables
b)
Express one variable in terms of the other
c)
Add the equations together
d)
Multiply the equations by a common factor
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Foothill Academy answered |
The first step in the substitution method is to express one variable in terms of the other. This allows for substitution into the second equation, simplifying the system to a single-variable equation that can be easily solved.
If you have two equations, \( x + y = 10 \) and \( 2x - y = 3 \), what is one way to eliminate \( y \)?- a) Divide both equations
- b) Multiply the first equation
- c) Substitute \( y \) from the first equation into the second
- d) Add the equations
Correct answer is option 'C'. Can you explain this answer?
If you have two equations, \( x + y = 10 \) and \( 2x - y = 3 \), what is one way to eliminate \( y \)?
a)
Divide both equations
b)
Multiply the first equation
c)
Substitute \( y \) from the first equation into the second
d)
Add the equations
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Foothill Academy answered |
To eliminate \( y \), one effective method is to substitute \( y \) from the first equation \( y = 10 - x \) into the second equation. This will simplify the problem into a single variable equation.
In a problem involving ages, if A's present age is \( x \) and B's age is \( y \), and they are in a ratio of 9:4, what is the equation representing this relationship?- a) \( x + y = 13 \)
- b) \( 9x - 4y = 0 \)
- c) \( x/y = 9/4 \)
- d) \( 4x - 9y = 0 \)
Correct answer is option 'B'. Can you explain this answer?
In a problem involving ages, if A's present age is \( x \) and B's age is \( y \), and they are in a ratio of 9:4, what is the equation representing this relationship?
a)
\( x + y = 13 \)
b)
\( 9x - 4y = 0 \)
c)
\( x/y = 9/4 \)
d)
\( 4x - 9y = 0 \)
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Foothill Academy answered |
The correct representation of A's age \( x \) and B's age \( y \) in a ratio of 9:4 is \( 9x - 4y = 0 \). This equation can be used in conjunction with another equation to find the actual ages.
Which of the following methods is most useful for solving equations with variables in denominators?- a) Cross-multiplication
- b) Guess and check
- c) Graphing
- d) Simple elimination
Correct answer is option 'A'. Can you explain this answer?
Which of the following methods is most useful for solving equations with variables in denominators?
a)
Cross-multiplication
b)
Guess and check
c)
Graphing
d)
Simple elimination
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Foothill Academy answered |
Cross-multiplication is particularly effective for solving equations with variables in denominators. It allows for a straightforward approach to eliminate the fractions, transforming the equation into a more manageable form.
Which method uses a formula to directly find the values of \( x \) and \( y \) from two equations?- a) Cross-multiplication
- b) Elimination
- c) Substitution
- d) Graphical method
Correct answer is option 'A'. Can you explain this answer?
Which method uses a formula to directly find the values of \( x \) and \( y \) from two equations?
a)
Cross-multiplication
b)
Elimination
c)
Substitution
d)
Graphical method
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Foothill Academy answered |
The cross-multiplication method utilizes a specific formula to find the values of \( x \) and \( y \) directly from two linear equations. By identifying the coefficients and applying the formula, one can solve for both variables efficiently.
If the equations are \( 3x - 4y = 10 \) and \( 5x - 3y = 24 \), what is the first step in the elimination method?- a) Solve for \( x \)
- b) Add the equations together
- c) Substitute \( y \) in terms of \( x \)
- d) Multiply the equations to make coefficients equal
Correct answer is option 'D'. Can you explain this answer?
If the equations are \( 3x - 4y = 10 \) and \( 5x - 3y = 24 \), what is the first step in the elimination method?
a)
Solve for \( x \)
b)
Add the equations together
c)
Substitute \( y \) in terms of \( x \)
d)
Multiply the equations to make coefficients equal
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Foothill Academy answered |
The first step in using the elimination method for these equations is to multiply one or both equations to make the coefficients of either \( x \) or \( y \) equal, allowing for elimination when the equations are added or subtracted.
When using the method of elimination by equating coefficients, what is primarily done to the original equations?- a) Variables are substituted to simplify the equations
- b) The equations are added together
- c) One or both equations are multiplied to make coefficients equal
- d) They are graphed to find the intersection point
Correct answer is option 'C'. Can you explain this answer?
When using the method of elimination by equating coefficients, what is primarily done to the original equations?
a)
Variables are substituted to simplify the equations
b)
The equations are added together
c)
One or both equations are multiplied to make coefficients equal
d)
They are graphed to find the intersection point
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Foothill Academy answered |
In the method of elimination by equating coefficients, one or both equations are multiplied by necessary factors to make the coefficients of one variable equal. This allows for elimination through addition or subtraction of the equations, leading to a simpler equation to solve.
What is the standard form of a linear equation?- a) \( ax + by + c = 0 \)
- b) \( ax + by = c \)
- c) \( ax^2 + by + c = 0 \)
- d) \( ax + by + c = 1 \)
Correct answer is option 'A'. Can you explain this answer?
What is the standard form of a linear equation?
a)
\( ax + by + c = 0 \)
b)
\( ax + by = c \)
c)
\( ax^2 + by + c = 0 \)
d)
\( ax + by + c = 1 \)
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Foothill Academy answered |
The standard form of a linear equation is \( ax + by + c = 0 \), where \( a \), \( b \), and \( c \) are real numbers, and \( x \) and \( y \) are variables. This format is essential as it allows for easy identification of the coefficients and constant, which aids in graphing and solving the equation.
If the cost price of an item is \( x \) and the selling price is \( y \), and the profit percentage is given, how would you express this relationship?- a) \( y = x + profit \)
- b) \( y = x - (profit \% \times x) \)
- c) \( y = x - profit \)
- d) \( y = x + (profit \% \times x) \)
Correct answer is option 'D'. Can you explain this answer?
If the cost price of an item is \( x \) and the selling price is \( y \), and the profit percentage is given, how would you express this relationship?
a)
\( y = x + profit \)
b)
\( y = x - (profit \% \times x) \)
c)
\( y = x - profit \)
d)
\( y = x + (profit \% \times x) \)
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Foothill Academy answered |
The relationship between cost price \( x \) and selling price \( y \) can be expressed as \( y = x + (profit \% \times x) \). This shows that the selling price is the cost price plus the profit made on it.
What is the solution for the equations \( x + y = 7 \) and \( x - y = 1 \)?- a) \( x = 3, y = 4 \)
- b) \( x = 5, y = 2 \)
- c) \( x = 4, y = 3 \)
- d) \( x = 2, y = 5 \)
Correct answer is option 'C'. Can you explain this answer?
What is the solution for the equations \( x + y = 7 \) and \( x - y = 1 \)?
a)
\( x = 3, y = 4 \)
b)
\( x = 5, y = 2 \)
c)
\( x = 4, y = 3 \)
d)
\( x = 2, y = 5 \)
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Foothill Academy answered |
Adding the equations gives \( 2x = 8 \) or \( x = 4 \). Substituting \( x = 4 \) into \( x + y = 7 \) gives \( y = 3 \). Therefore, the solution is \( x = 4, y = 3 \).
How do you express one variable in terms of another in the equation \( x + y = 7 \)?- a) \( x = 7 + y \)
- b) \( y = 7 - x \)
- c) \( y = x - 7 \)
- d) \( x = 7 - y \)
Correct answer is option 'B'. Can you explain this answer?
How do you express one variable in terms of another in the equation \( x + y = 7 \)?
a)
\( x = 7 + y \)
b)
\( y = 7 - x \)
c)
\( y = x - 7 \)
d)
\( x = 7 - y \)
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Foothill Academy answered |
To express \( y \) in terms of \( x \) from the equation \( x + y = 7 \), you rearrange it to get \( y = 7 - x \). This expression is crucial for methods like substitution.
In the context of simultaneous equations, what does the term "solution" refer to?- a) Any point on the graph
- b) The constants in the equations
- c) A pair of values that satisfy all equations
- d) The coefficients of the equations
Correct answer is option 'C'. Can you explain this answer?
In the context of simultaneous equations, what does the term "solution" refer to?
a)
Any point on the graph
b)
The constants in the equations
c)
A pair of values that satisfy all equations
d)
The coefficients of the equations
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Foothill Academy answered |
In simultaneous equations, the "solution" refers to the specific pair of values for the variables that satisfy all equations in the system. This means that these values make all the equations true simultaneously.
What is a common real-life application of simultaneous linear equations?- a) Solving quadratic equations
- b) Determining quantities in budgeting
- c) Calculating interest rates
- d) Finding the area of a triangle
Correct answer is option 'B'. Can you explain this answer?
What is a common real-life application of simultaneous linear equations?
a)
Solving quadratic equations
b)
Determining quantities in budgeting
c)
Calculating interest rates
d)
Finding the area of a triangle
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Foothill Academy answered |
Simultaneous linear equations are commonly used in real-life situations such as budgeting, where one might need to determine how to allocate a fixed amount of money across multiple expenses, like tickets and snacks.
In a problem where the ages of two individuals are given in a ratio, what is the first step in forming equations?- a) Define the variables for their ages
- b) Identify the sum of their ages
- c) Solve for their ages
- d) Find the difference in their ages
Correct answer is option 'A'. Can you explain this answer?
In a problem where the ages of two individuals are given in a ratio, what is the first step in forming equations?
a)
Define the variables for their ages
b)
Identify the sum of their ages
c)
Solve for their ages
d)
Find the difference in their ages
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Foothill Academy answered |
The first step in solving age-related problems presented in a ratio is to define variables for the ages involved. This allows for the formulation of equations based on the relationships described.
If the product of two fractions results in 1, what can be inferred about the fractions?- a) They are both positive
- b) They are both negative
- c) They are equal
- d) They are reciprocals
Correct answer is option 'D'. Can you explain this answer?
If the product of two fractions results in 1, what can be inferred about the fractions?
a)
They are both positive
b)
They are both negative
c)
They are equal
d)
They are reciprocals
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Foothill Academy answered |
If the product of two fractions equals 1, it indicates that they are reciprocals of each other. For example, \( \frac{a}{b} \times \frac{b}{a} = 1 \).
If the sum of two numbers is 12 and their difference is 2, what are the two numbers?- a) 7 and 5
- b) 6 and 6
- c) 4 and 8
- d) 5 and 7
Correct answer is option 'A'. Can you explain this answer?
If the sum of two numbers is 12 and their difference is 2, what are the two numbers?
a)
7 and 5
b)
6 and 6
c)
4 and 8
d)
5 and 7
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Foothill Academy answered |
Let the two numbers be \( x \) and \( y \). The equations formed are \( x + y = 12 \) and \( x - y = 2 \). Adding these gives \( 2x = 14 \) or \( x = 7 \). Substituting \( x \) back into the first equation gives \( y = 5 \). Thus, the numbers are 7 and 5.
What does the solution \( x = 2, y = 1 \) represent in terms of simultaneous equations?- a) Two independent equations
- b) The point of intersection of the two lines represented by the equations
- c) A single equation with infinite solutions
- d) A contradiction in the equations
Correct answer is option 'B'. Can you explain this answer?
What does the solution \( x = 2, y = 1 \) represent in terms of simultaneous equations?
a)
Two independent equations
b)
The point of intersection of the two lines represented by the equations
c)
A single equation with infinite solutions
d)
A contradiction in the equations
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Foothill Academy answered |
The solution \( x = 2, y = 1 \) represents the point of intersection of the two lines defined by the simultaneous equations. This point signifies the values of \( x \) and \( y \) that satisfy both equations simultaneously.
Chapter doubts & questions for Simultaneous Equations - Mathematics for GCSE/IGCSE 2025 is part of Class 10 exam preparation. The chapters have been prepared according to the Class 10 exam syllabus. The Chapter doubts & questions, notes, tests & MCQs are made for Class 10 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests here.
Chapter doubts & questions of Simultaneous Equations - Mathematics for GCSE/IGCSE in English & Hindi are available as part of Class 10 exam.
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