Question

solve the following system of equations.
3x + 2y = -19
2x + 9y = -5
x =

y =

Explanation:

Step1: Eliminate a variable (e.g., x)

Multiply the first equation by 2: \(2(3x + 2y) = 2(-19)\) → \(6x + 4y = -38\)
Multiply the second equation by 3: \(3(2x + 9y) = 3(-5)\) → \(6x + 27y = -15\)

Step2: Subtract the equations

Subtract the first new equation from the second:
\((6x + 27y) - (6x + 4y) = -15 - (-38)\)
\(23y = 23\)

Step3: Solve for y

Divide both sides by 23: \(y = \frac{23}{23} = 1\)

Step4: Substitute y into an original equation

Use \(3x + 2y = -19\) with \(y = 1\):
\(3x + 2(1) = -19\) → \(3x + 2 = -19\)
Subtract 2: \(3x = -21\)
Divide by 3: \(x = -7\)

Answer:

\(x = -7\), \(y = 1\)