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.
\[

$$\begin{align*} (3x + 8y) + (2x - 8y) &= 15 + 10\\ 3x + 2x + 8y - 8y &= 25\\ 5x &= 25 \end{align*}$$

\]

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:

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