Question

How maNY solutions do these equations have? No solution, one solution, infinite solutions.

a) y = 2x + 3 and y = -2x + 11

b) y = x + 2 and -2x + 2y = 4

c) y = x - 3 and y = x + 6

d) y = 7 and y =3x-5

e) y = -4x and y = -4x - 1
​

Answer 1

See below.

Explanation:

a) y = 2x + 3 and y = -2x + 11

One solution. They are straight lines with different slopes, so they will intersect at some point.

b) y = x + 2 and -2x + 2y = 4

-2x + 2y = 4 can be rearranged to 2y = 2x +4 and then y = x + 4

Both lines have the same slope, 1. They are parallel and will never meet. No solutions.

c) y = x - 3 and y = x + 6

This has the same answer as c. Parallel lines (both have slopes of 1.). They will never meet: no solutions.

d) y = 7 and y =3x-5

One solution. Straight lines with different slopes (3 and 0) so they will cross at one point. [At (4,7)]

e) y = -4x and y = -4x - 1

Same slopes. There are no solutions.