  ### Home > INT1 > Chapter 6 > Lesson 6.3.3 > Problem6-107

6-107.

Determine the point of intersection of each pair of lines if one exists. Be sure to record your process on your paper. Check each solution, if possible.

1. $x = −2y − 3$
$4y − x = 9$

The three methods you can choose from are: Equal Value, Substitution, or Elimination.
Review the Math Notes box in section 6.2.1, 6.2.3, and 6.3.3

Perhaps the Substitution Method would be best here since one of the equations has already been solved for $x$.

$4y − x = 9$ Substitute $− 2y − 3$ for $x$
$4y − \left(− 2y − 3\right) = 9$

$4y + 2y + 3 = 9$
$6y + 3 = 9$

$(-5,1)$ is the solution.

1. $x + 5y = 8$
$−x + 2y = −1$

The three methods you can choose from are: Equal Value, Substitution, or Elimination.
Review the Math Notes box in section 6.2.1, 6.2.3, and 6.3.3

Use the Elimination Method.

1. $4x − 2y = 5$
$y = 2x + 10$

Using the Substitution Method results in $−20 = 5$, which is clearly impossible, therefore, there is no solution to this system of equations.