Question

solve using elimination.
x - 6y = -19
-10x - 9y = -17
(□, □)

Explanation:

Step1: Multiply first equation by 10

To eliminate \(x\), multiply the first equation \(x - 6y=-19\) by 10. We get \(10x-60y = - 190\).

Step2: Add to second equation

Now add this new equation to the second equation \(-10x - 9y=-17\).
\((10x-60y)+(-10x - 9y)=-190+(-17)\)
Simplify left side: \(10x-10x-60y - 9y=-69y\)
Right side: \(-190 - 17=-207\)
So, \(-69y=-207\).

Step3: Solve for y

Divide both sides by \(-69\): \(y=\frac{-207}{-69}=3\).

Step4: Substitute y into first equation

Substitute \(y = 3\) into \(x-6y=-19\): \(x-6\times3=-19\)
\(x - 18=-19\)
Add 18 to both sides: \(x=-19 + 18=-1\).

Answer:

\((-1, 3)\)