Algebra 1 question

Question

Identify the integers that y=2x-1 and y=kx + 3. will have 1 possible solution, no solution, and infinite solutions (3 different sets of solutions). If possible, please show steps as I do not understand and am not sure how to even start the problem. Thank you!!

Answer 1

Algebra 1 question

Identify the integers that y=2x-1 and y=kx + 3. will have 1 possible solution, no solution, and infinite solutions (3 different sets of solutions). If possible, please show steps as I do not understand and am not sure how to even start the problem. Thank you!!

Hello Jennifer,

Both lines will never intersect if they have the same slopes.

So, if k = 2, there are NO Solutions.

There is exactly 1 solution, where the lines intersect at:

y = 2x - 1

y = kx + 3

Set equal to each other:

Solve for x:

2x - 1 = kx + 3

2x - kx = 4

x(2 - k) =4

x = 4/(2 - k)

k ≠ 2

1 intersection at the point [4/(2 - k), 2(4/(2 - k)) -1]

An infinite number of solutions exists when the equations for the lines are exaclty the same:

y = 2x - 1

y = kx + 3

Set equal to each other:

2x - 1 = kx + 3

Solve for k:

2x - 1 -3 = kx

2x - 4 = kx

k = (2x - 4)/x

Infinite Solutions

when k = (2x - 4)/x

x ≠ 0

Any questions?

Answer 2

1 solution, different slopes, different intercepts

no solution, same slope, different intercepts

all solutions, same slope, same intercepts