Question

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 ...?

Answer 1

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