Consider the following system of equations y=3x-7, y-3x=5. What can you conclude about the system of equations?

Question

Consider the following system of equations y=3x-7, y-3x=5. What can you conclude about the system of equations?

Answer 1

y = mx + b is an equation of the line with slope m and y-intercept b.  

 

y = 3x - 7 has slope 3 and y-intercept -7

y = 3x + 5 has slope 3 and y-intercept 5

 

The lines have the same slope but have different y-intercepts.

 

So, the lines are parallel.

 

The solutions of the system of equations are the points where the graphs intersect.

 

Since the lines are parallel, they do not intersect.

 

Therefore, the system of equations has no solution.  

 

 

Answer 2

Timothy

 

If you rearrange your second equation to y = 3x + 5 you will see that your two equations are very similar, they are both in the form of slope intercept lines.  Their slopes are the same, each has a slope of 3 and only the y intercept is different, where these equations cross the y intercept when x = 0.  Two lines with the same slope are parallel lines.

 

Best of luck,

 

Lori