Answer:
The correct option is d.
Step-by-step explanation:
The given equations are
[tex]x-2y=2[/tex] .... (1)
[tex]y=-2x+5[/tex] .... (2)
In equation 2, multiply both sides by 2.
[tex]2y=-4x+10[/tex] .... (3)
Now add equation (1) and (3).
[tex]x-2y+2y=2+(-4x+10)[/tex]
[tex]x=2-4x+10[/tex]
[tex]x+4x=12[/tex]
[tex]5x=12[/tex]
Divide both sides by 5.
[tex]x=\frac{12}{5}=2.4[/tex]
Put this value in equation (2).
[tex]y=-2(2.4)+5[/tex]
[tex]y=-4.8+5[/tex]
[tex]y=0.2[/tex]
Therefore the solution of the system of equation is (2.4,0.2) and the system has only one solution. Option d is correct.
