In Example 8, by changing what one number in the first equation does the system become 

(a) Inconsistent? 

(b) Consistent?

Data from Example 8

Solve the system of equations x − 3y = 9 −2x + 6y = −18. 

We find that the intercepts and a third point for the first line are (9, 0), (0, −3), and (3, −2). For the second line, we then find that the intercepts are the same as for the first line. We also find that the check point (3, −2) also satisfies the equation of the second line. This means that the two lines are really the same line. Another check is to write each equation in slope-intercept form. This gives us the equation y = 1/3x − 3 for each line. See Fig. 5.21.

2 0 -2 -4 y Same line for both equations 5 Fig. 5.21 10 X