To solve the system of equations:
[tex]\[
\begin{cases}
2x - 5y = -26 \\
y = 1 - x
\end{cases}
\][/tex]
we can use the substitution method. Here are the detailed steps:
1. Express one variable in terms of the other: The second equation is already solved for [tex]\( y \)[/tex]:
[tex]\[
y = 1 - x
\][/tex]
2. Substitute this expression into the first equation: Substitute [tex]\( y = 1 - x \)[/tex] into [tex]\( 2x - 5y = -26 \)[/tex]:
[tex]\[
2x - 5(1 - x) = -26
\][/tex]
3. Simplify and solve for [tex]\( x \)[/tex]:
[tex]\[
2x - 5 + 5x = -26
\][/tex]
Combining like terms:
[tex]\[
7x - 5 = -26
\][/tex]
Add 5 to both sides:
[tex]\[
7x = -21
\][/tex]
Divide by 7:
[tex]\[
x = -3
\][/tex]
4. Find [tex]\( y \)[/tex] using the value of [tex]\( x \)[/tex]: Substitute [tex]\( x = -3 \)[/tex] back into [tex]\( y = 1 - x \)[/tex]:
[tex]\[
y = 1 - (-3) = 1 + 3 = 4
\][/tex]
So, the value of [tex]\( y \)[/tex] that is part of the solution is [tex]\( y = 4 \)[/tex].
The solution to the system of equations is:
[tex]\[
(-3, 4)
\][/tex]
Hence, the value of [tex]\( y \)[/tex] that is part of the solution is [tex]\( y = 4 \)[/tex].
The solution is [tex]\( (-3, 4) \)[/tex].
