Question

Question
Solve the system of equations.
–x+6y=13

4x–10y=–10
(1 point)
(
,
)

Answer 1

To solve the system of equations:

1. \(-x + 6y = 13\) (Equation 1)
2. \(4x - 10y = -10\) (Equation 2)

We can use either substitution or elimination. Here, I'll use the substitution method.

First, let's solve Equation 1 for \(x\):

\[
-x + 6y = 13
\]

Add \(x\) to both sides:

\[
6y = x + 13
\]

Now, let's isolate \(x\):

\[
x = 6y - 13
\]

Now, we can substitute \(x\) in Equation 2:

\[
4(6y - 13) - 10y = -10
\]

Distribute \(4\):

\[
24y - 52 - 10y = -10
\]

Combine like terms:

\[
(24y - 10y) - 52 = -10
\]
\[
14y - 52 = -10
\]

Now, add \(52\) to both sides:

\[
14y = 42
\]

Now, divide by \(14\):

\[
y = 3
\]

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

\[
x = 6(3) - 13
\]
\[
x = 18 - 13
\]
\[
x = 5
\]

Thus, the solution to the system of equations is:

\[
(x, y) = (5, 3)
\]

So the answer is \((5, 3)\).