Question

Which system of equations below has no solution?

A. y = 4x + 5 and y = 4x – 5
B. y = 4x + 5 and 2y = 8x + 10
C. y = 4x + 5 and y = 1/4 + 5
D. y = 4x + 5 and y = 8x + 10

Answer 1

A. 4x+5=4x-5
4x+10=4x
10=0

B. 4x+5=4x+5

C.4x+5=1/4+5
4x=1/4
16x=1
x=16

D. 4x+5=8x+10
-4x=5
x=-5/4

A. has no solution

Answer 2

A. y = 4x + 5 and y = 4x – 5

Explanation:

If the system of equations have the same slope and different y-intercept, then it will have no solution.

From the given options, let's find the slope and y-intercept.

A. y = 4x + 5 and y = 4x - 5

Slope = 4 and y-intercepts are 5 and -5

Here we have the same slope and different y-intercepts. So, this is systems of equations have no solution.

B. y = 4x + 5 and 2y = 8x + 10 => y = 4x + 5

Both are the same equations.

This system has an infinite number of solutions.

The answer is A) y = 4x + 5 and y = 4x – 5