Question

solve using elimination.
-x - 4y = -19
-6x - 8y = -2

Explanation:

Step1: Multiply first equation by 2

To eliminate \( y \), multiply the first equation \(-x - 4y = -19\) by 2. We get \( -2x - 8y = -38 \).

Step2: Subtract the new equation from the second equation

The second equation is \(-6x - 8y = -2\). Subtract \(-2x - 8y = -38\) from \(-6x - 8y = -2\):
\((-6x - 8y) - (-2x - 8y) = -2 - (-38)\)
Simplify: \(-6x - 8y + 2x + 8y = -2 + 38\)
Which gives \(-4x = 36\).

Step3: Solve for \( x \)

Divide both sides of \(-4x = 36\) by \(-4\): \( x = \frac{36}{-4} = -9 \).

Step4: Substitute \( x = -9 \) into first equation

Substitute \( x = -9 \) into \(-x - 4y = -19\): \(-(-9) - 4y = -19\)
Simplify: \( 9 - 4y = -19 \).

Step5: Solve for \( y \)

Subtract 9 from both sides: \(-4y = -19 - 9 = -28\)
Divide by \(-4\): \( y = \frac{-28}{-4} = 7 \).

Answer:

\((-9, 7)\)