Question

Which system of linear equations has no solutions?

a) y = 4x +1 y= -4x + 1
b) y= 2x + 7 y= 2x - 7
c) 3x + y =1 6x + 2y =2
d) 5x + y =3 x + 5y = 15

Answer 1

b)

Explanation:

a) y = 4x +1 y= -4x + 1

Different slopes; same y-intercept; lines intersect at 1 point; there is 1 solution.

b) y= 2x + 7 y= 2x - 7

Same slopes; different y-intercepts; parallel lines do not intersect; no solution.

c) 3x + y =1 6x + 2y =2

Equations are the same; infinite number of solutions.

d) 5x + y =3 x + 5y = 15

Different slopes; lines intersect at 1 point; there is 1 solution.

Answer: b)