Solve the system of equations.

x=6y−3

2x+7y=13

1 answer

To solve the system of equations:

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

We can substitute the expression for \( x \) from Equation 1 into Equation 2.

Substituting \( x \) in Equation 2:

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

Now, simplify the left-hand side:

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

Combine like terms:

\[ 19y - 6 = 13 \]

Next, add 6 to both sides:

\[ 19y = 19 \]

Now, divide by 19:

\[ y = 1 \]

Now that we have \( y \), we can find \( x \) using Equation 1:

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

Thus, the solution to the system of equations is:

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