Question

The two lines graphed below are not parallel. How many solutions are there to the system of equations? 

Answer 1

Check picture below

what's the x,y ordered pair for that point?

Answer 2

Answer:

• The system of equation has a unique solution or one solution.

Option: A is the correct answer.

              A.  (-2,1)

Step-by-step explanation:

The solutions of the system of the equation are the possible points of the intersection of the two lines.

By looking at the graph of the functions the two lines are not parallel and the graph intersect at just one point.

Hence, the system of equations has just one solution or unique solution.

The system of equations is:

$y=\dfrac{1}{2}x+2$

and

$y=-2x-3$

The x-value of the point of intersection of two lines is calculated by equating both the lines i.e.

$\dfrac{1}{2}x+2=-2x-3\\\\i.e.\\\\\dfrac{1}{2}x+2x=-3-2\\\\i.e.\\\\\dfrac{5}{2}x=-5\\\\i.e.\\\\x=-2$

and when x= -2 then the value of y from first equation is:

$y=\dfrac{1}{2}\times (-2)+2\\\\i.e.\\\\y=-1+2\\\\i.e.\\\\y=1$

Hence, the solution is:

                       $(-2,1)$