Question

Which values of m and b will create a system of equations with no solution? Select two options. y = mx + b y = –2x + A

Answer 1

Answer:

(I can not see the options, so I will answer in a general way)

When we have a system of linear equations:

y = a*x + b

y = c*x + d

We have 3 possible options:

One solution: This happens when the lines intersect only one time, and the solution of the system is the point where the lines intersect.

No solutions: This happens when the lines do not intersect, is the case for parallel lines (lines with the same slope but different y-intercept)

Infinite solutions: This happens when the lines do intersect at infinite points, is the case for two equal lines (so both equations represent the same line)

Now we have the system:

y = m*x  + b

y = -2*x + A

We want to find values of m and b, such that this system has no solutions.

Then we know that the lines must be parallel, again, the lines must have the same slope but different y-intercept.

Then we can use:

m = -2, b = A + 1

we will get:

y = -2*x + (A + 1)

y = -2*x + A

This system has no solutions.

Other pair can be:

m = -2, b = A + 3

we will get

y = -2*x + (A + 3)

y = -2*x + A

This system has no solutions.