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 \((2)\):

$$
LATEXBLOCK0
$$

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 \(-3y + 5x = 26\):

$$
LATEXBLOCK1
$$

Subtract 6 from both sides:

$$ 5x=26 - 6=20 $$

Divide both sides by 5:

$$ x=\frac{20}{5}=4 $$

Answer:

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