Question

Solve the system by substitution.
minus, 3, y, plus, 10, equals, x
−3y+10=
x
10, x, plus, 7, y, equals, minus, 38
10x+7y=
−38
Answer
Attempt 1 out of 2

left parenthesis(
,
right parenthesis) Submit Answer

Answer 1

To solve the system of equations by substitution, we first rewrite the equations clearly:

1. \(-3y + 10 = x\)
2. \(10x + 7y = -38\)

Now we can start with the first equation. We can express \(x\) in terms of \(y\):

\[
x = -3y + 10
\]

Next, we substitute this expression for \(x\) into the second equation:

\[
10(-3y + 10) + 7y = -38
\]

Now, distribute \(10\) in the equation:

\[
-30y + 100 + 7y = -38
\]

Combine like terms:

\[
-30y + 7y + 100 = -38
\]

This simplifies to:

\[
-23y + 100 = -38
\]

Next, we subtract \(100\) from both sides:

\[
-23y = -38 - 100
\]
\[
-23y = -138
\]

Now, divide both sides by \(-23\):

\[
y = \frac{-138}{-23} = 6
\]

Now that we have \(y\), we can find \(x\) using the first equation \(x = -3y + 10\):

\[
x = -3(6) + 10
\]
\[
x = -18 + 10 = -8
\]

So the solution to the system of equations is:

\[
(x, y) = (-8, 6)
\]

The final answer is:

\[
\boxed{(-8, 6)}
\]