Question

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

Answer 1

To solve the given system of equations, we will use the substitution method. The equations are:

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

First, we will substitute the expression for \( x \) from the first equation into the second equation.

Substituting \( x = 6y - 3 \) into the second equation:

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

Now, let's simplify this equation:

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

Combine like terms:

\[
19y - 6 = 13
\]

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 \( x \):

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

Simplifying gives:

\[
x = 6 - 3 = 3
\]

Thus, the solution to the system of equations is:

\[
x = 3, \quad y = 1
\]

In summary, the solution is:

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