CPM Homework Help : INT3 Problem 3-83

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3-83.

Solve the following systems algebraically. What does each solution reveal about the graph of the equations in the system?

$x+2y=17$
$x-y=2$
Step 1 (a):
Multiply the second equation by $−1$ and use the Elimination Method.
$x+2y=17$
$−(x−y=2)$
Step 2 (a):
$x+2y=17$
$−x+y=−2$
Step 3 (a):
$3y=15$
$y=5$
Step 4 (a):
Substitute $5$ for $y$ in one equation to determine the value of $x$ .
Answer (a):
$(7,5)$

$4x+5y=11$
$2x+6y=16$
Hint (b):
See part (a).

$4x-3y=-10$
$x=\frac{1}{4}y-1$
Hint (c):
Substitute the expression for $x$ from the second equation into the first equation and solve.

$2x+y=-2x+5$
$3x+2y=2x+3y$
Hint (d):
Rewrite both equations in standard form.
Help (d):
See part (a).
Answer (d):
$(1,1)$

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