Question

solve the system of equations.

• 3y + 5x = 26
• 2y - 5x = -16

x =

y =

Explanation:

Step1: Add the two equations to eliminate \(x\)

The two equations are:
\(-3y + 5x = 26\) \((1)\)
\(-2y - 5x = -16\) \((2)\)

Adding \((1)\) and \((2)\):
\[

$$\begin{align*} (-3y + 5x)+(-2y - 5x)&=26+(-16)\\ -3y + 5x - 2y - 5x&=26 - 16\\ -5y&=10 \end{align*}$$

\]

Step2: Solve for \(y\)

From \(-5y = 10\), divide both sides by \(-5\):
\[
y=\frac{10}{-5}=-2
\]

Step3: Substitute \(y = -2\) into equation \((1)\) to solve for \(x\)

Substitute \(y=-2\) into \(-3y + 5x = 26\):
\[

$$\begin{align*} -3\times(-2)+5x&=26\\ 6 + 5x&=26 \end{align*}$$

\]

Subtract 6 from both sides:
\[
5x=26 - 6=20
\]

Divide both sides by 5:
\[
x=\frac{20}{5}=4
\]

Answer:

\(x = 4\)
\(y = -2\)