### Home > CC3MN > Chapter 9 > Lesson 9.1.1 > Problem9-13

9-13.

Determine by inspection whether the lines in each system below intersect, coincide, or are parallel. Do not actually solve the systems. Justify your reasons.

Parallel lines have equal slope.
Lines that coincide have equal slope and equal $y$-intercepts.
Lines that neither coincide or are parallel will intersect once.

1. $y = 2x + 3\\y=\frac { 1 } { 2 }x − 2$

The coefficient of $x$ tells you the slope.
Are they the same?

1. $2x + 3y = 6 \\2x + 3y = 9$

These equations have the same coefficient for $x$ and $y$, but have different constants. What does this tell you about that lines?

1. $y=\frac { 1 } { 3 }x + 2\\ y=\frac { 1 } { 3 }x - 2$

Notice that the coefficients of $x$ are the same in the two equations.

The lines are parallel.

1. $\:\:\:\:\:\:x - 2y = 4 \\-2x + 4y = -8$

Write both equations in $y = mx + b$ form.

$x − 2y = 4$

${\it y} = \frac{1}{2}{\it x} - 2$

$−2x + 4y = −8$

${\it y} = \frac{1}{2}{\it x} - 2$

Because the two equations are equal, the lines coincide.