Question

solve using substitution.
$x + y = -5$
$4x + 7y = -14$
(\boxed{\quad}, \boxed{\quad})$

Explanation:

Step1: Solve for x from the first equation

From \( x + y = -5 \), we can express \( x \) as \( x = -5 - y \).

Step2: Substitute x into the second equation

Substitute \( x = -5 - y \) into \( 4x + 7y = -14 \):
\[

$$\begin{align*} 4(-5 - y) + 7y &= -14\\ -20 - 4y + 7y &= -14\\ -20 + 3y &= -14 \end{align*}$$

\]

Step3: Solve for y

Add 20 to both sides:
\[
3y = -14 + 20 = 6
\]
Divide both sides by 3:
\[
y = \frac{6}{3} = 2
\]

Step4: Substitute y back to find x

Substitute \( y = 2 \) into \( x = -5 - y \):
\[
x = -5 - 2 = -7
\]

Answer:

\((-7, 2)\)