Question

Solve the system of linear equations using multiplication.

4x + 4y = 16
8x + 13y = 22

A. x = 2, y = 3
B. x = 1, y = 2
C. x = 3, y = 1
D. x = 4, y = 0

Answer 1

After multiplying the first equation by 2 and subtracting it from the second, we find that y = -2. Substituting y back into the first original equation, we solve for x and find it to be 6. Hence, the solution is x = 6 and y = -2, which is not listed in the provided options.

Step-by-step explanation:

To solve the system of linear equations using multiplication, you'll want to eliminate one variable by making the coefficients of either x or y equal. Let's take a look at the two equations given:

1. 4x + 4y = 16
2. 8x + 13y = 22

By multiplying the first equation by 2, we get:

• 8x + 8y = 32

Now we have the same coefficient for x in both equations:

1. 8x + 8y = 32
2. 8x + 13y = 22

By subtracting the first new equation from the second, we can eliminate x:

• (8x + 13y) - (8x + 8y) = 22 - 32
• 13y - 8y = -10
• 5y = -10
• y = -2

Now, substitute y = -2 into the first original equation:

• 4x + 4(-2) = 16
• 4x - 8 = 16
• 4x = 24
• x = 6

Therefore, the solution to the system is x = 6 and y = -2, which is not one of the provided options. It seems there may have been a mistake in the question or the provided options.