Question

solve by elimination: -x + 2y = 17; 2x + 2y = -10; options: (-9, -4), (9, -4), arn, (-9, 4)

Explanation:

Step1: Subtract the two equations

We have the system of equations:
$$-x + 2y = 17$$
$$2x + 2y = -10$$

Subtract the first equation from the second equation:
$$(2x + 2y) - (-x + 2y) = -10 - 17$$
Simplify the left side: \(2x + 2y + x - 2y = 3x\)
Simplify the right side: \(-27\)
So we get \(3x = -27\)

Step2: Solve for x

Divide both sides of \(3x = -27\) by 3:
\(x = \frac{-27}{3} = -9\)

Step3: Substitute x into one of the original equations

Substitute \(x = -9\) into the first equation \(-x + 2y = 17\):
\(-(-9) + 2y = 17\)
Simplify: \(9 + 2y = 17\)

Step4: Solve for y

Subtract 9 from both sides: \(2y = 17 - 9 = 8\)
Divide both sides by 2: \(y = \frac{8}{2} = 4\)

So the solution is \((-9, 4)\)

Answer:

\((-9, 4)\)