Question

solve using elimination.
4x - 5y = 12
9x - 10y = 17
( , )
submit

Explanation:

Step1: Multiply first equation by 2

To eliminate \( y \), we multiply the first equation \( 4x - 5y = 12 \) by 2. This gives us \( 8x - 10y = 24 \).

Step2: Subtract the two equations

Now we have two equations: \( 8x - 10y = 24 \) (from step 1) and \( 9x - 10y = 17 \) (original second equation). Subtract the first from the second: \( (9x - 10y) - (8x - 10y) = 17 - 24 \). Simplifying, we get \( x = -7 \).

Step3: Substitute x into first equation

Substitute \( x = -7 \) into \( 4x - 5y = 12 \). So, \( 4(-7) - 5y = 12 \), which simplifies to \( -28 - 5y = 12 \).

Step4: Solve for y

Add 28 to both sides: \( -5y = 12 + 28 = 40 \). Then divide by -5: \( y = \frac{40}{-5} = -8 \).

Answer:

\((-7, -8)\)