Question

Which ordered pair is the best estimate for the solution of the system of equations?

Answer 1

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.

$y=\frac{3}{2}x+6...(1)$

$y=\frac{1}{4}x-2...(2)$

We will use substitution method to solve our given system of equations.

Let us equate both equations to find the value of x.

$\frac{1}{4}x-2=\frac{3}{2}x+6$

$\frac{1}{4}x-\frac{3}{2}x-2=\frac{3}{2}x-\frac{3}{2}x+6$

$\frac{1}{4}x-\frac{3}{2}x-2=6$

$\frac{1}{4}x-\frac{3}{2}x-2+2=6+2$

$\frac{1}{4}x-\frac{3}{2}x=8$

Let us have common denominator.

$\frac{1}{4}x-\frac{3*2}{2*2}x=8$

$\frac{x}{4}-\frac{6x}{4}=8$

$\frac{x-6x}{4}=8$

$\frac{-5x}{4}=8$

$\frac{-5x}{4}*4=8*4$

$-5x=32$

$\frac{-5x}{-5}=\frac{32}{-5}$

$x=-6.4$

Upon substituting $x=-6.4$ in equation (1) we will get,

$y=\frac{3}{2}*(-6.4)+6$

$y=3*(-3.2)+6$

$y=-9.6+6$

$y=-3.6$

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.

Answer 2

This was the correct answer, I even provided proof from my own test. Hope this helps!