Question

How many solutions can be found for the system of linear equations represented on the graph?

Answer 1

Answer:

A) no solution

Step-by-step explanation:

These lines are parallel.  This means they never intersect; since the solution to a system of equations is the point or points of intersection, this means there is no solution to this system.

Answer 2

Answer: A) no solution

Step-by-step explanation:

The equation of first line = $y=-\dfrac{1}{2}x+4$

which can be written as : $2y=-x+8$

$x+2y=8$  

The equation of second line = $y=-\dfrac{1}{2}x-6$

which can be written as : $x+2y=-12$

Since , the ratio of the coefficients of x is equal to the ratio of the coefficients of y but not the ratio of the constants .

$\dfrac{1}{1}=\dfrac{2}{2}\neq\dfrac{8}{-12}$

Therefore , the lines are parallel and do not have any solution.

So , the correct answer is A) no solution.