Question

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

Answer 1

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

Answer 2

Answer:

The correct option is 2.

Step-by-step explanation:

The given system of equations is

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

$y=-2x+3$                  .... (2)

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

$y-y=\frac{1}{4}x-2-(-2x+3)$

$0=\frac{1}{4}x-2+2x-3$

On combining like terms we get

$0=\frac{9}{4}x-5$

Add 5 on both sides.

$5=\frac{9}{4}x$

Multiply both sides by 4.

$20=9x$

Divide both sides by 9.

$\frac{20}{9}=x$

The value of x is $\frac{20}{9}$.

Substitute $x=\frac{20}{9}$ in equation (2).

$y=-2(\frac{20}{9})+3=-\frac{13}{9}$

The solution of given system of equation is

$(\frac{20}{9},-\frac{13}{9})=(2.22...,-1.44...)\approx (2.2,-1.4)$

Therefore the correct option is 2.