Question

solve.
-5x + 7y = 12
-2x + 3y = 4
(□, □)

Explanation:

Step1: Eliminate x by multiplying equations

Multiply the first equation \(-5x + 7y = 12\) by 2: \(2(-5x + 7y)=2\times12\) → \(-10x + 14y = 24\)
Multiply the second equation \(-2x + 3y = 4\) by 5: \(5(-2x + 3y)=5\times4\) → \(-10x + 15y = 20\)

Step2: Subtract the two new equations

Subtract \(-10x + 14y = 24\) from \(-10x + 15y = 20\):
\((-10x + 15y)-(-10x + 14y)=20 - 24\)
Simplify: \(y=-4\)

Step3: Substitute y into one equation

Substitute \(y = -4\) into \(-2x + 3y = 4\):
\(-2x + 3(-4)=4\) → \(-2x - 12 = 4\)

Step4: Solve for x

Add 12 to both sides: \(-2x=4 + 12\) → \(-2x=16\)
Divide by -2: \(x=\frac{16}{-2}=-8\)

Answer:

\((-8, -4)\)