To solve the system of linear equations
[tex]\[
\left\{
\begin{array}{l}
2x - y = 11 \\
x + 3y = -5
\end{array}
\right.
\][/tex]
we can follow these steps:
1. Isolate one variable in one of the equations:
Take the first equation: [tex]\( 2x - y = 11 \)[/tex].
Solve for [tex]\( y \)[/tex]:
[tex]\[
y = 2x - 11
\][/tex]
2. Substitute this expression into the second equation:
Now we substitute [tex]\( y = 2x - 11 \)[/tex] into the second equation [tex]\( x + 3y = -5 \)[/tex]:
[tex]\[
x + 3(2x - 11) = -5
\][/tex]
3. Solve for [tex]\( x \)[/tex]:
Simplify the equation:
[tex]\[
x + 6x - 33 = -5
\][/tex]
Combine like terms:
[tex]\[
7x - 33 = -5
\][/tex]
Add 33 to both sides:
[tex]\[
7x = 28
\][/tex]
Divide by 7:
[tex]\[
x = 4
\][/tex]
4. Substitute [tex]\( x \)[/tex] back into the expression for [tex]\( y \)[/tex]:
We previously found [tex]\( y = 2x - 11 \)[/tex]. Now substitute [tex]\( x = 4 \)[/tex]:
[tex]\[
y = 2(4) - 11
\][/tex]
Simplify:
[tex]\[
y = 8 - 11
\][/tex]
[tex]\[
y = -3
\][/tex]
Therefore, the value of [tex]\( y \)[/tex] is [tex]\( -3 \)[/tex].
