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Solve the following system of equations by substitution.
$$
\begin{array}{c}
-x+y=-5 \\
2 x-5 y=1
\end{array}
$$
in Mathematics by Gold Status (10,098 points) | 37 views

1 Answer

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Best answer
First, we will solve the first equation for $y$.
$$
\begin{array}{l}
-x+y=-5 \\
y=x-5
\end{array}
$$
Now, we can substitute the expression $x-5$ for $y$ in the second equation.
$$
\begin{array}{l}
2 x-5 y=1 \\
2 x-5(x-5)=1 \\
2 x-5 x+25=1 \\
-3 x=-24 \\
x=8
\end{array}
$$
Now, we substitute $x=8$ into the first equation and solve for $y$.
$$
-(8)+y=-5
$$
$$
y=3
$$
Our solution is $(8,3)$.
Check the solution by substituting $(8,3)$ into both equations.
$$
\begin{array}{l}
-x+y=-5 \\
-(8)+(3)=-5
\end{array}
$$
True
$$
2 x-5 y=1
$$
$$
2(8)-5(3)=1
$$
True
The substitution method can be used to solve any linear system in two variables, but the method works best if one of the equa-
tions contains a coefficient of 1 or $-1$ so that we do not have to deal with fractions.
by Gold Status (10,098 points)

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