CPM Homework Help : CC3MN Problem 10-103

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.

$x = −2y − 3$
$4y − x = 9$
Hint (a):
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
More Help (a):
Perhaps the Substitution Method would be best here since one of the equations has already been solved for $x$ .
Step 1(a):
$4y − x = 9$ Substitute $− 2y − 3$ for $x$
$4y − \left(− 2y − 3\right) = 9$
Step 2(a):
$4y + 2y + 3 = 9$
$6y + 3 = 9$
Answer (a):
$(-5,1)$ is the solution.

$x + 5y = 8$
$−x + 2y = −1$
Hint (b):
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
More Help:
Use the Elimination Method.

$4x − 2y = 5$
$y = 2x + 10$
Answer (c):
Using the Substitution Method results in $−20 = 5$ , which is clearly impossible, therefore, there is no solution to this system of equations.