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Question 392568: use substitution to solve for x and y
y+2x=12
x+2y=12
Answer by haileytucki(390)   (Show Source):
You can put this solution on YOUR website! y+2x=12_x+2y=12
Since 2x does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 2x from both sides.
y=-2x+12_x+2y=12
Replace all occurrences of y with the solution found by solving the last equation for y. In this case, the value substituted is -2x+12.
y=-2x+12_x+2(-2x+12)=12
Multiply 2 by each term inside the parentheses.
y=-2x+12_x-4x+24=12
Since x and -4x are like terms, add -4x to x to get -3x.
y=-2x+12_-3x+24=12
Since 24 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 24 from both sides.
y=-2x+12_-3x=-24+12
Add 12 to -24 to get -12.
y=-2x+12_-3x=-12
Divide each term in the equation by -3.
y=-2x+12_-(3x)/(-3)=-(12)/(-3)
Simplify the left-hand side of the equation by canceling the common factors.
y=-2x+12_x=-(12)/(-3)
Simplify the right-hand side of the equation by simplifying each term.
y=-2x+12_x=4
Replace all occurrences of x with the solution found by solving the last equation for x. In this case, the value substituted is 4.
y=-2(4)+12_x=4
Multiply -2 by each term inside the parentheses.
y=-8+12_x=4
Add 12 to -8 to get 4.
y=4_x=4
This is the solution to the system of equations.
y=4_x=4
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