Question

Which solution is the best estimate to the system of equations?

○(1.5, 0)
○(2.2, -1.4)
○(0,3)
○(0, -2)

{y=1/4x-2
{y=-2x+3

Answer 1

(1.5,0) ? I'm not sure...

Answer 2

The correct option is 2.

Explanation:

The given system of equations is

`y=(1)/(4)x-2` .... (1)

`y=-2x+3` .... (2)

Subtract equation (2) from equation (1), to eliminate y.

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

`0=(1)/(4)x-2+2x-3`

On combining like terms we get

`0=(9)/(4)x-5`

Add 5 on both sides.

`5=(9)/(4)x`

Multiply both sides by 4.

`20=9x`

Divide both sides by 9.

`(20)/(9)=x`

The value of x is
`(20)/(9)`.

Substitute
`x=(20)/(9)` in equation (2).

`y=-2((20)/(9))+3=-(13)/(9)`

The solution of given system of equation is

`((20)/(9),-(13)/(9))=(2.22...,-1.44...)\approx (2.2,-1.4)`

Therefore the correct option is 2.