Question

5x+2y=10
x+ay=4
Which value of a makes these equations have no solution.

Answer 1

2

Explanation:

Rearrange to same form:

2y = -5x + 10

y = -5/2x + 10

ay = -5x + 4

Parallel lines have no intersection and solution, thus a = 2

Answer 2

Explanation:

For there to be no solution the lines must be parallel and have different y intercepts. To be parallel they must have the same slope.

Solving each for y

y=(10-5x)/2 and y=(4-x)/a

So the slopes are

-5/2 and -1/a, if they are equal

-5/2=-1/a

-5a=-2

a=2/5