Question

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

y =

Explanation:

Step1: Eliminate x by multiplying equations

Multiply the first equation by 2 and the second by 5:
First equation: \(2(-5x - 9y) = 2(-2)\) → \(-10x - 18y = -4\)
Second equation: \(5(2x + 5y) = 5(5)\) → \(10x + 25y = 25\)

Step2: Add the two new equations

Add \(-10x - 18y = -4\) and \(10x + 25y = 25\):
\((-10x + 10x) + (-18y + 25y) = -4 + 25\)
\(7y = 21\)

Step3: Solve for y

Divide both sides by 7:
\(y = \frac{21}{7} = 3\)

Step4: Substitute y into one equation

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

Step5: Solve for x

Subtract 15: \(2x = 5 - 15 = -10\)
Divide by 2: \(x = \frac{-10}{2} = -5\)

Answer:

\(x = -5\)
\(y = 3\)