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solve x and y x÷6+y÷4=1 and 3x÷4- x-y÷2=7÷4 Related: Substitution M...
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solve x and y x÷6+y÷4=1 and 3x÷4- x-y÷2=7÷4 Related: Substitution M...
Substitution Method - Pair of Linear Equations in Two Variables
Step 1: Simplify the given equations to their standard form.
x/6 + y/4 = 1 (Equation 1)
3x/4 - x - y/2 = 7/4 (Equation 2)
Multiplying both sides of Equation 1 by 12, we get:
2x + 3y = 24 (Equation 3)
Multiplying both sides of Equation 2 by 4, we get:
3x - 4x - 2y = 7 (Equation 4)
Simplifying Equation 4, we get:
-x - 2y = 7 (Equation 5)
Step 2: Solve for one variable in terms of the other in one of the equations.
From Equation 5, we get:
x = -7 - 2y (Equation 6)
Step 3: Substitute the expression for the variable found in step 2 into the other equation.
Substituting Equation 6 into Equation 3, we get:
2(-7 - 2y) + 3y = 24
Simplifying the equation, we get:
-14 - 4y + 3y = 24
Simplifying further, we get:
-y = 38
Therefore, y = -38.
Step 4: Substitute the value found in step 3 into one of the equations to find the other variable.
Substituting y = -38 into Equation 6, we get:
x = -7 - 2(-38)
Simplifying the equation, we get:
x = 69
Therefore, x = 69 and y = -38 are the solutions to the given pair of linear equations.
Step 1: Simplify the given equations to their standard form.
x/6 + y/4 = 1 (Equation 1)
3x/4 - x - y/2 = 7/4 (Equation 2)
Multiplying both sides of Equation 1 by 12, we get:
2x + 3y = 24 (Equation 3)
Multiplying both sides of Equation 2 by 4, we get:
3x - 4x - 2y = 7 (Equation 4)
Simplifying Equation 4, we get:
-x - 2y = 7 (Equation 5)
Step 2: Solve for one variable in terms of the other in one of the equations.
From Equation 5, we get:
x = -7 - 2y (Equation 6)
Step 3: Substitute the expression for the variable found in step 2 into the other equation.
Substituting Equation 6 into Equation 3, we get:
2(-7 - 2y) + 3y = 24
Simplifying the equation, we get:
-14 - 4y + 3y = 24
Simplifying further, we get:
-y = 38
Therefore, y = -38.
Step 4: Substitute the value found in step 3 into one of the equations to find the other variable.
Substituting y = -38 into Equation 6, we get:
x = -7 - 2(-38)
Simplifying the equation, we get:
x = 69
Therefore, x = 69 and y = -38 are the solutions to the given pair of linear equations.
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solve x and y x÷6+y÷4=1 and 3x÷4- x-y÷2=7÷4 Related: Substitution Method - Pair of Linear Equations in Two Variables? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about solve x and y x÷6+y÷4=1 and 3x÷4- x-y÷2=7÷4 Related: Substitution Method - Pair of Linear Equations in Two Variables? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for solve x and y x÷6+y÷4=1 and 3x÷4- x-y÷2=7÷4 Related: Substitution Method - Pair of Linear Equations in Two Variables?.
solve x and y x÷6+y÷4=1 and 3x÷4- x-y÷2=7÷4 Related: Substitution Method - Pair of Linear Equations in Two Variables? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about solve x and y x÷6+y÷4=1 and 3x÷4- x-y÷2=7÷4 Related: Substitution Method - Pair of Linear Equations in Two Variables? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for solve x and y x÷6+y÷4=1 and 3x÷4- x-y÷2=7÷4 Related: Substitution Method - Pair of Linear Equations in Two Variables?.
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