Question

solve the following system of equations.
-7x - 3y = -2
-9x - 7y = -12
x =

y =

Explanation:

Step1: Eliminate y by multiplying equations

Multiply the first equation \(-7x - 3y = -2\) by 7: \(-49x - 21y = -14\).
Multiply the second equation \(-9x - 7y = -12\) by 3: \(-27x - 21y = -36\).

Step2: Subtract the two new equations

Subtract the second new equation from the first:
\((-49x - 21y) - (-27x - 21y) = -14 - (-36)\)
Simplify: \(-22x = 22\).

Step3: Solve for x

Divide both sides by -22: \(x = \frac{22}{-22} = -1\).

Step4: Substitute x into first original equation

Substitute \(x = -1\) into \(-7x - 3y = -2\):
\(-7(-1) - 3y = -2\) → \(7 - 3y = -2\).

Step5: Solve for y

Subtract 7: \(-3y = -9\).
Divide by -3: \(y = 3\).

Answer:

\(x = -1\), \(y = 3\)