Question

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

y=32x+6
y=14x−2

A(−6, −3)

B(−6.5, −3.5)

C(−7, −4)

D(−7, −3.5)

Answer 1

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

Answer 2

B. (−6.5, −3.5)

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=(3)/(2)x+6...(1)`

`y=(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.

`(1)/(4)x-2=(3)/(2)x+6`

`(1)/(4)x-(3)/(2)x-2=(3)/(2)x-(3)/(2)x+6`

`(1)/(4)x-(3)/(2)x-2=6`

`(1)/(4)x-(3)/(2)x-2+2=6+2`

`(1)/(4)x-(3)/(2)x=8`

Let us have common denominator.

`(1)/(4)x-(3*2)/(2*2)x=8`

`(x)/(4)-(6x)/(4)=8`

`(x-6x)/(4)=8`

`(-5x)/(4)=8`

`(-5x)/(4)*4=8*4`

`-5x=32`

`(-5x)/(-5)=(32)/(-5)`

`x=-6.4`

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

`y=(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.