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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

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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

User Barbara Morris
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