Which graph below shows a system of equations with no solution?

Consider two equation of line

1. A x + B y = C

2. P x + Q y = R

→A system of equation in two variable has no solution only when the two lines never intersect , i.e they are parallel to each other.

i.e⇒

Or in another term

y = m x + c ------(1)

y = k x + r -----(2)

If slope of two lines are same i.e, m=k, then the two lines are parallel having no solution.

Equation of line having X intercept (a,0) and Y intercept (0,b) is given by

x/a  + y\b= 1

Graph 1:

Line 1.  x + y = 2 As line passes through (2,0) and (0,2).

Line 2.  x + y = -2 As line passes through (-2,0) and (0,-2).

Slope of both the lines are -1. So line (1) and line (2) are parallel.It has no solution.

In Graph 2 and 4 it is open that two lines are intersecting having one solution.

In Graph 3 , the two lines are coincident i.e infinite number of solution.

So , Option (1) i.e Graph 1  Consist of two lines which have no solution.

the correct answer is 5 6 and 7