### Home > CC3 > Chapter Ch9 > Lesson 9.2.1 > Problem9-63

9-63.

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

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.