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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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