### Home > INT3 > Chapter 3 > Lesson 3.2.1 > Problem3-83

3-83.

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

1. $x+2y=17$
$x-y=2$

Multiply the second equation by $−1$ and use the Elimination Method.

$x+2y=17$
$−(x−y=2)$

$x+2y=17$
$−x+y=−2$

$3y=15$
$y=5$

Substitute $5$ for $y$ in one equation to determine the value of $x$.

$(7,5)$

1. $4x+5y=11$
$2x+6y=16$

See part (a).

1. $4x-3y=-10$
$x=\frac{1}{4}y-1$

Substitute the expression for $x$ from the second equation into the first equation and solve.

1. $2x+y=-2x+5$
$3x+2y=2x+3y$

Rewrite both equations in standard form.

See part (a).

$(1,1)$