Question

Question Solve the system of equations.
x=6y−3
2x+7y=13

Answer 1

To solve the system of equations:

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

We will substitute Equation 1 into Equation 2.

Substituting \( x \) from Equation 1 into Equation 2 gives:

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

Now, distribute the 2:

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

Combine like terms:

\[
19y - 6 = 13
\]

Add 6 to both sides:

\[
19y = 19
\]

Now divide by 19:

\[
y = 1
\]

Now that we have \( y \), we will substitute it back into Equation 1 to find \( x \):

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

\[
x = 6 - 3
\]

\[
x = 3
\]

The solution to the system of equations is:

\[
(x, y) = (3, 1)
\]

Thus, the solution is \( x = 3 \) and \( y = 1 \).