To solve the system of equations:
[tex]\[
\left\{
\begin{array}{l}
2x + y = -4 \\
3x + 5y = 29
\end{array}
\right.
\][/tex]
we need to find values for [tex]\(x\)[/tex] and [tex]\(y\)[/tex] that satisfy both equations simultaneously. Here are the steps:
1. Express [tex]\(y\)[/tex] from the first equation:
[tex]\[
2x + y = -4 \implies y = -4 - 2x
\][/tex]
2. Substitute [tex]\(y\)[/tex] into the second equation:
Substitute [tex]\( y = -4 - 2x \)[/tex] into [tex]\( 3x + 5y = 29 \)[/tex]:
[tex]\[
3x + 5(-4 - 2x) = 29
\][/tex]
3. Simplify the equation:
[tex]\[
3x - 20 - 10x = 29
\][/tex]
Combine like terms:
[tex]\[
-7x - 20 = 29
\][/tex]
4. Solve for [tex]\(x\)[/tex]:
Add 20 to both sides:
[tex]\[
-7x = 49
\][/tex]
Divide both sides by -7:
[tex]\[
x = -7
\][/tex]
5. Find [tex]\(y\)[/tex] using the value of [tex]\(x\)[/tex]:
Substitute [tex]\(x = -7\)[/tex] back into the expression for [tex]\(y\)[/tex]:
[tex]\[
y = -4 - 2(-7)
\][/tex]
Simplify:
[tex]\[
y = -4 + 14 = 10
\][/tex]
So, the solution to the system of equations is:
[tex]\[
x = -7, \quad y = 10
\][/tex]
Therefore, the values are [tex]\(\boxed{x = -7}\)[/tex] and [tex]\(\boxed{y = 10}\)[/tex].
