Question

determine if the following system of equations have no solutions in infinity solutions or exactly one solution 2x + y = -2x + y = -6 what is the answer

Answer 1

Let:

`\begin{gathered} 2x+y=4_{\text{ }}(1) \\ -2x+y=-6_{\text{ }}(2) \end{gathered}`

Using elimination method:

`\begin{gathered} (1)+(2) \\ 2x+(-2x)+y+y=4+(-6) \\ 2y=-2 \\ y=-(2)/(2) \\ y=-1 \end{gathered}`

Replace the value of y into (1):

`\begin{gathered} 2x+(-1)=4 \\ 2x=4+1 \\ 2x=5 \\ x=(5)/(2)=2.5 \end{gathered}`

The solution is:

`((5)/(2),-1)`

Therefore the system has one solution