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