Solve using the substitution method. Show your work. If the system has no solution or an infinite number of solutions, state this.

15x + 9y = 240

6x + 3y = 90 ... ?

The answer is x = 10, y = 10.

Step 1: rearrange the second equation for y.

Step 2: substitute y from the second equation into the first equation.

Step 3. Calculate y.

Step 1.

The second equation is: 6x + 3y = 90

Divide both sides of the equation by 3:

(6x + 3y) / 3 = 90/3

6x/3 + 3y/3 = 30

2x + y = 30

Rearrange the equation:

y = 30 - 2x

Step 2.

Substitute y from the second equation (y = 30 - 2x) into the first equation:

15x + 9y = 240

15x + 9 (30 - 2x) = 240

15x + 270 - 18x = 240

15x - 18x = 240 - 270

-3x = - 30

x = - 30/-3

x = 10

Step 3.

Since y = 30 - 2x and x = 10, then:

y = 30 - 2 * 10

y = 30 - 20

y = 10