Question

use substitution to solve the system.

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$$\begin{cases} y = 3x - 13 \\\\ -4x + 5y = -21 \\end{cases}$$

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\\(x = \square\\)
\\(y = \square\\)

Explanation:

Substitute the expression for y into the second equation

We are given the system of equations:

$$
LATEXBLOCK0
$$

Substitute \(y = 3x - 13\) into the second equation:

$$ -4x + 5(3x - 13) = -21 $$

Expand the equation using the distributive property

Using the Distributive Property:

$$ -4x + 15x - 65 = -21 $$

Solve the linear equation for x

Using Linear Equation Solutions:

$$
LATEXBLOCK1
$$

Substitute the value of x back to find y

Substitute \(x = 4\) into the first equation:

$$
LATEXBLOCK2
$$

Answer:

Use substitution to solve the system.

$$
LATEXBLOCK0
$$

\(x =\) <blank>4</blank>
\(y =\) <blank>-1</blank>