Question

solve the system of linear equations by elimination.
$2x + 5y = 16$
$3x - 5y = -1$
solution: (\square, \square)

Explanation:

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

The two equations are \( 2x + 5y = 16 \) and \( 3x - 5y = -1 \). When we add them together, the \( 5y \) and \( -5y \) terms will cancel out.
\[

$$\begin{align*} (2x + 5y) + (3x - 5y) &= 16 + (-1)\\ 2x + 5y + 3x - 5y &= 15\\ 5x &= 15 \end{align*}$$

\]

Step2: Solve for \( x \)

Divide both sides of the equation \( 5x = 15 \) by 5.
\[
x=\frac{15}{5}=3
\]

Step3: Substitute \( x = 3 \) into one of the original equations to find \( y \)

Let's use the first equation \( 2x + 5y = 16 \). Substitute \( x = 3 \) into it:
\[

$$\begin{align*} 2(3)+5y&=16\\ 6 + 5y&=16 \end{align*}$$

\]
Subtract 6 from both sides:
\[
5y=16 - 6=10
\]
Divide both sides by 5:
\[
y = \frac{10}{5}=2
\]

Answer:

\((3, 2)\)