Question

Solve the system of equations.
x=6y−3

2x+7y=13
(1 point)

Answer 1

To solve the system of equations, we'll substitute the expression for \( x \) from the first equation into the second equation.

The first equation is:
\[
x = 6y - 3
\]

The second equation is:
\[
2x + 7y = 13
\]

Now, substitute \( x \) from the first equation into the second equation:

\[
2(6y - 3) + 7y = 13
\]

Now, simplify the equation:

\[
12y - 6 + 7y = 13
\]

Combine like terms:

\[
19y - 6 = 13
\]

Add 6 to both sides:

\[
19y = 19
\]

Now, divide by 19:

\[
y = 1
\]

Next, substitute \( y = 1 \) back into the first equation to find \( x \):

\[
x = 6(1) - 3 = 6 - 3 = 3
\]

Thus, the solution to the system of equations is:
\[
(x, y) = (3, 1)
\]

So the final answer is:
\[
\boxed{(3, 1)}
\]