What is the standard form of a linear equation?

Ax + by + c = 0

Which method involves expressing one variable in terms of another in simultaneous equations? A) Method of substitution B) Method of elimination C) Method of coefficients D) Method of cross-multiplication

A) Method of substitution

Riddle: I am a method that eliminates variables by making coefficients equal, what am I?

Method of elimination by equating coefficients

True or False: The solution to simultaneous equations is a single value for each variable.

False. The solution is a pair of values for the variables that satisfy all equations in the system.

The method of solving simultaneous equations where one equation is multiplied to match coefficients is called ______.

Method of elimination by equating coefficients

If x + y = 12 and x - y = 2, what are the values of x and y? (Choose the correct pair) A) x = 5, y = 7 B) x = 7, y = 5 C) x = 6, y = 6 D) x = 10, y = 2

B) x = 7, y = 5

What is the method called that uses the formula to solve equations of the standard form?

Method of cross-multiplication

Riddle: I can simplify a fraction's numerator and denominator, but I need a clever substitution to do so. What am I?

Equations reducible to linear equations

True or False: The sum of the variables in a two-digit number can be directly expressed as an equation.

True.

Fill in the blank: To find the cost price and selling price based on profit percentages, one can set up equations involving ______.

C.P. and S.P.

What type of problems involve determining ages based on given ratios or differences over time?

Problems based on ages

If A's age is 18 years, what is the ratio of A's age to B's age if B's age is 8 years?

9:4

Which method can be used to solve the equations 2/x + 3/y = 6 and 6/x - 5/y = 4 by simplifying variables?

Equations reducible to linear equations

Multiple Choice: In which method do you substitute one variable back into an equation after finding the other? A) Equating coefficients B) Cross-multiplication C) Substitution D) Elimination

C) Substitution

True or False: The problems based on fractions involve finding a fraction where the numerator and denominator satisfy certain conditions.

True.

Fill in the blank: The equations formed in problems based on two-digit numbers involve the tens and units digits, which can be represented as ______.

X and y

If two numbers have a sum of 12 and a difference of 2, what are the two numbers?

7 and 5

Which type of problem can involve time taken by individuals to complete work based on their combined work rates?

Problems based on time and work

Riddle: I am two numbers that when added give 12, but when subtracted give 2. What are my values?

7 and 5

What is the general form of a linear equation?

Ax + by + c = 0