Question

solve the system of two equations using substitution. -4x + 6y = 38
x - 5y = -20

Answer 1

To solve the system of equations using substitution, we have the following two equations:

1) \(-4x + 6y = 38\)
2) \(x - 5y = -20\)

First, let's solve the second equation for \(x\):

\[
x - 5y = -20
\]
\[
x = -20 + 5y
\]

Now we can substitute this expression for \(x\) into the first equation:

\[
-4(-20 + 5y) + 6y = 38
\]

Distributing \(-4\):

\[
80 - 20y + 6y = 38
\]

Now, combine like terms (\(-20y + 6y\)):

\[
80 - 14y = 38
\]

Next, isolate the \(y\) term by subtracting 80 from both sides:

\[
-14y = 38 - 80
\]
\[
-14y = -42
\]

Now, divide both sides by \(-14\):

\[
y = \frac{-42}{-14} = 3
\]

Now that we have the value of \(y\), we can substitute it back into the equation for \(x\):

\[
x = -20 + 5y
\]
\[
x = -20 + 5(3)
\]
\[
x = -20 + 15
\]
\[
x = -5
\]

Therefore, the solution to the system of equations is:

\[
\boxed{(-5, 3)}
\]