Question

solve using elimination.
7x - 8y = -10
-10x + 9y = -10
(□, □)

Explanation:

Step1: Multiply equations to eliminate x

Multiply the first equation \(7x - 8y = -10\) by 10: \(70x - 80y = -100\).
Multiply the second equation \(-10x + 9y = -10\) by 7: \(-70x + 63y = -70\).

Step2: Add the two new equations

Add \(70x - 80y = -100\) and \(-70x + 63y = -70\):
\((70x - 70x) + (-80y + 63y) = -100 + (-70)\)
Simplify: \(-17y = -170\)

Step3: Solve for y

Divide both sides by -17: \(y = \frac{-170}{-17} = 10\)

Step4: Substitute y into first equation

Substitute \(y = 10\) into \(7x - 8y = -10\):
\(7x - 8(10) = -10\)
\(7x - 80 = -10\)
Add 80 to both sides: \(7x = 70\)
Divide by 7: \(x = 10\)

Answer:

\((10, 10)\)