Question

solve the following system of equations.
-3x - 2y = 5
8x + 5y = -15
x =

y =

Explanation:

Step1: Eliminate y by multiplying equations

Multiply the first equation \(-3x - 2y = 5\) by 5: \(-15x - 10y = 25\)
Multiply the second equation \(8x + 5y = -15\) by 2: \(16x + 10y = -30\)

Step2: Add the two new equations

Add \(-15x - 10y = 25\) and \(16x + 10y = -30\):
\((-15x + 16x) + (-10y + 10y) = 25 + (-30)\)
\(x = -5\)

Step3: Substitute x into one equation

Substitute \(x = -5\) into \(-3x - 2y = 5\):
\(-3(-5) - 2y = 5\)
\(15 - 2y = 5\)

Step4: Solve for y

Subtract 15 from both sides: \(-2y = 5 - 15\)
\(-2y = -10\)
Divide by -2: \(y = 5\)

Answer:

\(x = -5\)
\(y = 5\)