Question

solve using elimination.
-x - 4y = -19
6x + 5y = 19
(\boxed{ }, \boxed{ })
submit

Explanation:

Step1: Multiply first equation by 6

To eliminate \(x\), we multiply the first equation \(-x - 4y=-19\) by 6. This gives us:
\(6\times(-x - 4y)=6\times(-19)\)
\(-6x-24y = - 114\)

Step2: Add to second equation

Now we add this new equation \(-6x - 24y=-114\) to the second equation \(6x + 5y = 19\).
\((-6x-24y)+(6x + 5y)=-114 + 19\)
The \(x\) terms cancel out: \(-6x+6x=0\), so we have \(-19y=-95\)

Step3: Solve for y

Divide both sides of \(-19y=-95\) by \(-19\):
\(y=\frac{-95}{-19}=5\)

Step4: Substitute y into first equation

Substitute \(y = 5\) into the first equation \(-x-4y=-19\):
\(-x-4\times5=-19\)
\(-x - 20=-19\)
Add 20 to both sides: \(-x=-19 + 20=1\)
Multiply both sides by - 1: \(x=-1\)

Answer:

\((-1, 5)\)