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.

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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:

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Subtract 6 from both sides:

$$ 5y=16 - 6=10 $$

Divide both sides by 5:

$$ y = \frac{10}{5}=2 $$

Answer:

\((3, 2)\)