Question 269163: Solve this equation using the substitution method.
9x - 2y = 3
3x - 6 = y
Answer by persian52(161)   (Show Source):
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9x-2y=3_3x-6=y
Since y is on the right-hand side of the equation, switch the sides so it is on the left-hand side of the equation.
9x-2y=3_y=3x-6
Replace all occurrences of y with the solution found by solving the last equation for y. In this case, the value substituted is 3x-6.
9x-2(3x-6)=3_y=3x-6
Multiply -2 by each term inside the parentheses.
9x+(-6x+12)=3_y=3x-6
Since 9x and -6x are like terms, add -6x to 9x to get 3x.
3x+12=3_y=3x-6
Since 12 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 12 from both sides.
3x=-12+3_y=3x-6
Add 3 to -12 to get -9.
3x=-9_y=3x-6
Divide each term in the equation by 3.
(3x)/(3)=-(9)/(3)_y=3x-6
Simplify the left-hand side of the equation by canceling the common terms.
x=-(9)/(3)_y=3x-6
Simplify the right-hand side of the equation by simplifying each term.
x=-3_y=3x-6
Replace all occurrences of x with the solution found by solving the last equation for x. In this case, the value substituted is -3.
x=-3_y=3(-3)-6
Multiply 3 by each term inside the parentheses.
x=-3_y=-9-6
Subtract 6 from -9 to get -15.
x=-3_y=-15
This is the solution to the system of equations.
Answers: x=-3, y=-15
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