2x-3y=21,y=3-x
Replace all occurrences of y with the solution found by solving the last equation for y. In this case, the value substituted is -x+3.
2x-3(-x+3)=21, y=-x+3
Multiply -3 by each term inside the parentheses.
2x+(3x-9)=21_y=-x+3
Since 2x and 3x are like terms, add 3x to 2x to get 5x.
5x-9=21, y=-x+3
Since -9 does not contain the variable to solve for, move it to the right-hand side of the equation by adding 9 to both sides.
5x=9+21, y=-x+3
Add 21 to 9 to get 30.
5x=30, y=-x+3
Divide each term in the equation by 5.
(5x)/(5)=(30)/(5)_y=-x+3
Simplify the left-hand side of the equation by canceling the common terms.
x=(30)/(5), y=-x+3
Simplify the right-hand side of the equation by simplifying each term.
x=6_y=-x+3
Replace all occurrences of x with the solution found by solving the last equation for x. In this case, the value substituted is 6.
x=6, y=-(6)+3
Multiply -1 by the 6 inside the parentheses.
x=6, y=-6+3
Add 3 to -6 to get -3.
x=6, y=-3
This is the solution to the system of equations.
x=6, y=-3