Question

solve the following system of equations.
-5x + 3y = -3
3x - 5y = 21
x =

y =

Explanation:

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

Multiply the first equation \(-5x + 3y = -3\) by 3: \(-15x + 9y = -9\)
Multiply the second equation \(3x - 5y = 21\) by 5: \(15x - 25y = 105\)

Step2: Add the two new equations

\((-15x + 9y) + (15x - 25y) = -9 + 105\)
Simplify: \(-16y = 96\)

Step3: Solve for y

Divide both sides by -16: \(y = \frac{96}{-16} = -6\)

Step4: Substitute y into an original equation

Use \(3x - 5y = 21\). Substitute \(y = -6\):
\(3x - 5(-6) = 21\)
\(3x + 30 = 21\)

Step5: Solve for x

Subtract 30: \(3x = 21 - 30 = -9\)
Divide by 3: \(x = \frac{-9}{3} = -3\)

Answer:

\(x = -3\), \(y = -6\)