Question

solve the system of equations.
3x + 8y = 15
2x - 8y = 10
x =

y =

Explanation:

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

The two equations are \( 3x + 8y = 15 \) and \( 2x - 8y = 10 \). When we add them together, the \( 8y \) and \( -8y \) terms will cancel out.

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Step2: Solve for \( x \)

Divide both sides of the equation \( 5x = 25 \) by 5.

$$ x = \frac{25}{5} = 5 $$

Step3: Substitute \( x = 5 \) into one of the original equations to solve for \( y \)

Let's use the first equation \( 3x + 8y = 15 \). Substitute \( x = 5 \) into it:

$$ 3(5) + 8y = 15\\ 15 + 8y = 15 $$

Subtract 15 from both sides:

$$ 8y = 15 - 15\\ 8y = 0 $$

Divide both sides by 8:

$$ y = \frac{0}{8} = 0 $$

Answer:

\( x = 5 \)
\( y = 0 \)