Question

Which of the systems of linear equations will have no solution?

Question 15 options:

y = 12 – 3x

y = 2x – 3


y = x – 1

-5x + y = -5


2x + y = 9

2x + y = 5


y = 2x

3x + 2y = 21

Answer 1

2x + y = 9

2x + y = 5

Explanation:

No solutions for 2 lines will only happen when the lines are parallel and never touch. So there are no solutions.

Lines are parallel when slopes are the same.

The equations cannot be the same just the slopes are the same.

Let's rearrange this set of equations into y=mx+b so we can see what the slope m is:

2x + y = 9 and 2x + y = 5

y= -2x +9 y= - 2x +5

You can see the lines are different but have the slopes so they are parallel and no solutions.

Answer 2

Answer: The third one

Explanation:

That system has the same equation, but a different solution, meaning the lines can never intersect.

We can also convert it into slope-intercept form.

y = -2x + 9

y = -2x + 5

Different slope and same y-intercept = NO SOLUTION