Question

Use the substitution method to solve the system 2x+2y=6 , 3x+2y=9 .(1 point)

Answer 1

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.