Question

solve using substitution.

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$$\begin{aligned} 5x - 8y &= -1 \\\\ 2x + y &= -13 \\end{aligned}$$

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Explanation:

🆕 New Concept Discovered: Solving Systems of Equations by Substitution
Replacing one variable with an equivalent expression

Step 1: Isolate a variable

We look for the easiest variable to isolate. In the second equation, \( y \) has a coefficient of \( 1 \), so we solve for \( y \):

$$ 2x + y = -13 \implies y = -2x - 13 $$

Step 2: Substitute into the other equation

We substitute the expression for \( y \) into the first equation:

$$ 5x - 8(-2x - 13) = -1 $$

Step 3: Solve for \( x \)

Distribute and combine like terms:

$$ 5x + 16x + 104 = -1 $$

$$ 21x + 104 = -1 $$

$$ 21x = -105 $$

$$ x = -5 $$

Step 4: Solve for \( y \)

Substitute \( x = -5 \) back into our expression for \( y \):

$$ y = -2(-5) - 13 $$

$$ y = 10 - 13 $$

$$ y = -3 $$

Answer:

\( (-5, -3) \)