Question

find the solution of the system of equations.\

$$\begin{cases}-3x - 5y = -28\\\\-3x + 4y = 17\\end{cases}$$

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show your work here\
x = \
y = \
check

Explanation:

Step1: Subtract the two equations

Subtract the second equation from the first to eliminate \(x\).
\((-3x - 5y) - (-3x + 4y) = -28 - 17\)
Simplify: \(-3x - 5y + 3x - 4y = -45\)
Which gives: \(-9y = -45\)

Step2: Solve for \(y\)

Divide both sides by \(-9\): \(y = \frac{-45}{-9} = 5\)

Step3: Substitute \(y\) into one equation

Use the first equation \(-3x - 5y = -28\). Substitute \(y = 5\):
\(-3x - 5(5) = -28\)
Simplify: \(-3x - 25 = -28\)
Add 25 to both sides: \(-3x = -3\)
Divide by \(-3\): \(x = 1\)

Answer:

\(x = 1\), \(y = 5\)