To find the value of [tex]\( y \)[/tex] in the given system of equations:
[tex]\[
\begin{align*}
3x - 4y &= -20 \quad \text{(Equation 1)} \\
-x + 2y &= 10 \quad \text{(Equation 2)}
\end{align*}
\][/tex]
Follow these steps:
1. Solve for one variable in terms of the other using one of the equations.
From Equation 2, isolate [tex]\( x \)[/tex]:
[tex]\[
-x + 2y = 10
\][/tex]
Add [tex]\( x \)[/tex] to both sides:
[tex]\[
2y = x + 10
\][/tex]
Subtract 10 from both sides:
[tex]\[
x = 2y - 10
\][/tex]
2. Substitute this expression for [tex]\( x \)[/tex] into Equation 1.
Substitute [tex]\( x = 2y - 10 \)[/tex] into [tex]\( 3x - 4y = -20 \)[/tex]:
[tex]\[
3(2y - 10) - 4y = -20
\][/tex]
Expand the equation:
[tex]\[
6y - 30 - 4y = -20
\][/tex]
Combine like terms:
[tex]\[
2y - 30 = -20
\][/tex]
3. Solve for [tex]\( y \)[/tex].
Add 30 to both sides:
[tex]\[
2y = 10
\][/tex]
Divide both sides by 2:
[tex]\[
y = 5
\][/tex]
Thus, the value of [tex]\( y \)[/tex] in the given system of equations is:
[tex]\[
\boxed{5}
\][/tex]
