Question

solve using elimination.
3x - y = -16
4x - 3y = -13
( , )
submit

Explanation:

Step1: Multiply first equation by 3

To eliminate \( y \), we multiply the first equation \( 3x - y = -16 \) by 3. This gives us \( 9x - 3y = -48 \).

Step2: Subtract the second equation

Now we subtract the second equation \( 4x - 3y = -13 \) from the new equation \( 9x - 3y = -48 \). So, \((9x - 3y) - (4x - 3y) = -48 - (-13)\). Simplifying the left side: \( 9x - 3y - 4x + 3y = 5x \). Simplifying the right side: \( -48 + 13 = -35 \). So we have \( 5x = -35 \).

Step3: Solve for x

Divide both sides of \( 5x = -35 \) by 5. So \( x = \frac{-35}{5} = -7 \).

Step4: Substitute x into first equation

Substitute \( x = -7 \) into the first equation \( 3x - y = -16 \). We get \( 3(-7) - y = -16 \), which simplifies to \( -21 - y = -16 \).

Step5: Solve for y

Add 21 to both sides: \( -y = -16 + 21 = 5 \). Multiply both sides by -1: \( y = -5 \).

Answer:

\((-7, -5)\)