Solve the system of equations.

x=6y−3

2x+7y=13
(1 poi

1 answer

To solve the system of equations given by the equations

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

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

Substituting \( x \) in the second equation:

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

Now distribute the \( 2 \):

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

Combine like terms:

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

Now, 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 find \( x \) using the first equation:

\[ x = 6y - 3 \]

Substituting \( y = 1 \) into the equation:

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

Thus, the solution to the system of equations is:

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