Answer:
B. (−6.5, −3.5)
Step-by-step explanation:
We have been given a system of equations and its graph and we are asked to choose the correct option that represents the solution of our given system.
[tex]y=\frac{3}{2}x+6...(1)[/tex]
[tex]y=\frac{1}{4}x-2...(2)[/tex]
We will use substitution method to solve our given system of equations.
Let us equate both equations to find the value of x.
[tex]\frac{1}{4}x-2=\frac{3}{2}x+6[/tex]
[tex]\frac{1}{4}x-\frac{3}{2}x-2=\frac{3}{2}x-\frac{3}{2}x+6[/tex]
[tex]\frac{1}{4}x-\frac{3}{2}x-2=6[/tex]
[tex]\frac{1}{4}x-\frac{3}{2}x-2+2=6+2[/tex]
[tex]\frac{1}{4}x-\frac{3}{2}x=8[/tex]
Let us have common denominator.
[tex]\frac{1}{4}x-\frac{3*2}{2*2}x=8[/tex]
[tex]\frac{x}{4}-\frac{6x}{4}=8[/tex]
[tex]\frac{x-6x}{4}=8[/tex]
[tex]\frac{-5x}{4}=8[/tex]
[tex]\frac{-5x}{4}*4=8*4[/tex]
[tex]-5x=32[/tex]
[tex]\frac{-5x}{-5}=\frac{32}{-5}[/tex]
[tex]x=-6.4[/tex]
Upon substituting [tex]x=-6.4[/tex] in equation (1) we will get,
[tex]y=\frac{3}{2}*(-6.4)+6[/tex]
[tex]y=3*(-3.2)+6[/tex]
[tex]y=-9.6+6[/tex]
[tex]y=-3.6[/tex]
We can also see from our given graph that at point (-6.5,-3.5) both lines intersect, therefore, the best estimate for our given system of equations is point (-6.5,-3.5) and option B is the correct choice.
