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 solve one equation for one variable and substitute that expression into the other equation.
Let's solve the first equation for x:
2x + 2y = 6
Subtract 2y from both sides:
2x = 6 - 2y
Divide both sides by 2:
x = 3 - y
Now substitute this expression for x into the second equation:
3(3 - y) + 2y = 9
Expand and simplify:
9 - 3y + 2y = 9
Combine like terms:
-y + 9 = 9
Subtract 9 from both sides:
-y = 0
Multiply both sides by -1 to eliminate the negative sign:
y = 0
Now substitute this value for y into the expression for x:
x = 3 - y
x = 3 - 0
x = 3
The solution to the system of equations is x = 3 and y = 0.