### Home > CC3 > Chapter 9 > Lesson 9.2.1 > Problem 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 ✎

*y*= 2*x*+ 3

*y*=*x*− 22

*x*+*y*= 6

2*x*+*y*= 9*y*=*x*+ 2

*y*=*x*− 2*x*− 2*y*= 4

−2*x*+ 4*y*= −8

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.

The coefficient of *x* tells you the slope.

Are they the same?

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

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

The lines are parallel.

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

*x* − 2*y* = 4

−2*x* + 4*y* = −8

Because the two equations are equal, the lines coincide.