Question

solve using elimination.\
-3x - 4y = -16\
-x + y = 18\
(\boxed{\quad}, \boxed{\quad})

Explanation:

Step1: Multiply the second equation by 4

To eliminate \( y \), we multiply the second equation \(-x + y = 18\) by 4. This gives us:
\( 4(-x + y) = 4\times18 \)
\( -4x + 4y = 72 \)

Step2: Add the two equations

Now we add the first equation \(-3x - 4y = -16\) and the new second equation \(-4x + 4y = 72\) together:
\((-3x - 4y) + (-4x + 4y) = -16 + 72\)
Simplifying the left side: \(-3x - 4x - 4y + 4y = -7x\)
Simplifying the right side: \(56\)
So we have \(-7x = 56\)

Step3: Solve for \( x \)

Divide both sides of \(-7x = 56\) by \(-7\):
\( x = \frac{56}{-7} = -8 \)

Step4: Substitute \( x = -8 \) into the second equation

Substitute \( x = -8 \) into \(-x + y = 18\):
\(-(-8) + y = 18\)
\(8 + y = 18\)

Step5: Solve for \( y \)

Subtract 8 from both sides:
\( y = 18 - 8 = 10 \)

Answer:

\((-8, 10)\)