Question

Shannon graphed the system of equations.

7x – 4y= –8
y = x – 3


what is the closest approximate solution to the system of equations?

(–5, –7.2)
(–5, –6.8)
(–5, –6.2)
(–5, –5.9)

Answer 1

we have

`7x - 4y= -8` -------> equation
`1`

`y = x - 3` -------> equation
`2`

Multiply the equation
`2` by
`4`

`4y = 4x - 12` -------> equation
`3`

Add equation equation
`1` and equation
`3`

`7x - 4y= -8\\4y = 4x - 12\\ -------\\7x=4x-20\\ 3x=-20\\ x=- (20)/(3)`

Find the value of y

`y = x - 3`

`y = - (20)/(3) - 3\\\\y = - (29)/(3)`

the solution is the point
`(-20/3,-29/3)----> (-6.67,-9.67)`

using a graph tool

see the attached figure

therefore

the answer is the option

(–5, –7.2)

Answer 2

All you need to do is plug -5 into the second equation and you see it is near (-5, -8). When plugged into the top, you get (-5, -27/4) which comes out to ABOUT -6.75 for the Y value. The closest is actually a tie. The first option is .8 from the first and .45 from the second leading in a total distance of 1.25. The second, which is the fellow answer, is 1.2 from the first and .05 from the second, leading to 1.25 away.

The third, which is next closest is 1.8 from the first and .55 from the second leading to a distance of over 2 from the optimal, so only the first two are answers.