Question

Solve the system of equations.
x=6y−3

2x+7y=13

Answer 1

To solve the system of equations:

1. \( x = 6y - 3 \)
2. \( 2x + 7y = 13 \)

We can start by substituting the expression for \( x \) from the first equation into the second equation.

Substitute \( x \) in the second equation:

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

Now distribute \( 2 \):

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

Combine like terms:

\[
(12y + 7y) - 6 = 13
\]
\[
19y - 6 = 13
\]

Next, add \( 6 \) to both sides:

\[
19y = 19
\]

Now, divide both sides by \( 19 \):

\[
y = 1
\]

Now that we have the value of \( y \), we can substitute it back into the first equation to find \( x \):

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

Thus, the solution to the system of equations is:

\[
\boxed{(3, 1)}
\]