Question

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

4x–10y=–10
(1 poi

Answer 1

To solve the system of equations

\[
-x + 6y = 13 \quad (1)
\]
\[
4x - 10y = -10 \quad (2)
\]

we will use the substitution or elimination method. Let's start by solving equation (1) for \(x\):

From equation (1):

\[
-x + 6y = 13
\]

We can rearrange it to express \(x\) in terms of \(y\):

\[
-x = 13 - 6y \implies x = 6y - 13
\]

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

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

Expanding the equation:

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

Combining like terms:

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

\[
14y - 52 = -10
\]

Adding 52 to both sides:

\[
14y = 42
\]

Dividing by 14:

\[
y = 3
\]

Now that we have \(y\), we can substitute \(y = 3\) back into the equation for \(x\):

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

Calculating:

\[
x = 18 - 13 = 5
\]

Thus, the solution to the system of equations is:

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