Use the substitution method to solve the system 2x+2y=6
, 3x+2y=9
.(1 point)
To solve the system using the substitution method, we need to solve one equation for one variable and substitute it into the other equation.
We can solve one equation for one variable as follows:
From the first equation, we can isolate x:
2x + 2y = 6
2x = 6 - 2y
x = (6 - 2y)/2
x = 3 - y
Now, we substitute this expression for x into the second equation:
3x + 2y = 9
3(3 - y) + 2y = 9
9 - 3y + 2y = 9
-y = 0
y = 0
Substitute this value of y into the expression for x:
x = 3 - y
x = 3 - 0
x = 3
Therefore, the solution to the system is x = 3 and y = 0.