Answer:
The correct option is 2.
Step-by-step explanation:
The given system of equations is
[tex]y=\frac{1}{4}x-2[/tex] .... (1)
[tex]y=-2x+3[/tex] .... (2)
Subtract equation (2) from equation (1), to eliminate y.
[tex]y-y=\frac{1}{4}x-2-(-2x+3)[/tex]
[tex]0=\frac{1}{4}x-2+2x-3[/tex]
On combining like terms we get
[tex]0=\frac{9}{4}x-5[/tex]
Add 5 on both sides.
[tex]5=\frac{9}{4}x[/tex]
Multiply both sides by 4.
[tex]20=9x[/tex]
Divide both sides by 9.
[tex]\frac{20}{9}=x[/tex]
The value of x is [tex]\frac{20}{9}[/tex].
Substitute [tex]x=\frac{20}{9}[/tex] in equation (2).
[tex]y=-2(\frac{20}{9})+3=-\frac{13}{9}[/tex]
The solution of given system of equation is
[tex](\frac{20}{9},-\frac{13}{9})=(2.22...,-1.44...)\approx (2.2,-1.4)[/tex]
Therefore the correct option is 2.
