Solve this System: 4x - 8y = 16 and -x - 2y = 24

To solve this system using the elimination method, we'll follow these steps:

• Step 1: Multiply the second equation by 4 to align the $x$-coefficients:

The second equation is $-x - 2y = 24$. Multiply it by 4:

$-4x - 8y = 96$

• Step 2: Add this to the first equation:

The first equation is $4x - 8y = 16$.

Adding the scaled second equation gives:

$(4x - 8y) + (-4x - 8y) = 16 + 96$

Solving gives:

$-16y = 112$

• Step 3: Solve for $y$:

Divide both sides by $-16$:

$y = \frac{112}{-16} = -7$

• Step 4: Substitute $y = -7$ into the original second equation:

Use $-x - 2y = 24$:

$-x - 2(-7) = 24$

$-x + 14 = 24$

Subtract 14 from both sides:

$-x = 10$

Multiply by $-1$:

$x = -10$

Thus, the solution to the system is $x = -10$ and $y = -7$.

Therefore, the solution to the problem is $(x, y) = (-10, -7)$.