Question

y = −2x − 3
y = −2x + 2
Are the graphs of the two lines intersecting lines, the same line, or parallel lines? Explain your reasoning.
How many solutions does the system have? Explain how you can tell without solving the system.

Answer 1

Solve the system using any method. Show your work.

{3x − 2y = 10
−1.5x + y= 5

Answer 2

1st
lines are parallel ... slopes are the same ... y-intercepts are different
... no solutions

2nd
multiplying the 2nd equation by -2 gives ... 3x - 2y = -10
... same result as 1st problem

Answer 3

All you have to do is look at the slopes of the two lines.
the first one has slope of 3
the 2nd has a slope of -1
So they clearly must intersect.