Question

solve the system using addition/elimination method. if there is exactly one solution, write as an ordered pair. if not, choose one of the other options.
{-4x - 8y = -24
{-x + 4y = 24

one solution:
no solution
infinite number of solutions
question help: video 1 video 2

Explanation:

Step1: Multiply second - equation

Multiply the second equation $-x + 4y=24$ by 4 to make the coefficients of $x$ in both equations opposite. We get $-4x+16y = 96$.

Step2: Subtract equations

Subtract the first equation $-4x - 8y=-24$ from the new - formed equation $-4x + 16y=96$.
$(-4x+16y)-(-4x - 8y)=96-(-24)$
$-4x+16y + 4x + 8y=96 + 24$
$24y=120$

Step3: Solve for $y$

Divide both sides of the equation $24y = 120$ by 24.
$y=\frac{120}{24}=5$

Step4: Substitute $y$ into second original equation

Substitute $y = 5$ into the second original equation $-x+4y = 24$.
$-x+4\times5=24$
$-x + 20=24$

Step5: Solve for $x$

Subtract 20 from both sides: $-x=24 - 20=4$, then multiply both sides by - 1 to get $x=-4$.

Answer:

One solution: $(-4,5)$