Question

Consider the following system of equations.

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.



Solve the system using any method. Show your work.

3x − 2y = 10
−1.5x + y = 5

Answer 1

in y = mx + b , (both of your equations are in that form)
m stands for the slope, and b is the y-intercept

They both have the same slope, so they must be parallel
One cuts the y-axis at -3, the other at 2

So what do you think???

for you second set of equations, arrange them in the form y = mx + b
to make your decision

Answer 2

The system of linear equations:
y = −2x − 3
y = −2x + 2.
What type of line (parallel, intersecting, and same) does this equation express?
Parallel Line: Same slope; Different y-intercepts.
Intersecting Line: Different slope; Different y-intercepts.
Same Line: Same slope; Same y-intercepts.
It is a parallel line since the slopes are the same, but the y-intercepts are different. Furthermore, it has no solution because parallel lines have a y-intercept (which is -1), but never has an intersection. Y=mx+b is a slope-intercept formula that may be used to solve the problem by graphing the lines.