Question

Solve using substitution.
x - 10y = 20
4x - 7y = -19
(_,_)

Answer 1

To solve the system of equations using substitution, we start with the two equations:

1. \( x - 10y = 20 \)
2. \( 4x - 7y = -19 \)

First, we can solve the first equation for \( x \):

\[
x = 10y + 20
\]

Next, we substitute \( x \) in the second equation:

\[
4(10y + 20) - 7y = -19
\]

Distributing \( 4 \) in the equation:

\[
40y + 80 - 7y = -19
\]

Now combine like terms:

\[
33y + 80 = -19
\]

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

\[
33y = -19 - 80
\]

\[
33y = -99
\]

Now, divide by \( 33 \) to solve for \( y \):

\[
y = -3
\]

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

\[
x = 10(-3) + 20
\]

\[
x = -30 + 20
\]

\[
x = -10
\]

Thus, the solution to the system of equations is:

\[
(x, y) = (-10, -3)
\]

So the answer is:

\[
\boxed{(-10, -3)}
\]