Given the system of equation
[tex]\begin{cases}-3x+y=19 \\ y=x+3\end{cases}[/tex]
Rewrite the equation above as
[tex]\begin{cases}-3x+y=19 \\ x-y=-3\end{cases}[/tex]
Using addition method, add the two equations to eliminate y
[tex]\begin{gathered} (-3x+x)+(y-y)=(19-3) \\ -2x=16 \\ \frac{-2x}{-2}=\frac{16}{-2} \\ x=-8 \end{gathered}[/tex]
Substitute x=-8 in the second equation to find y
[tex]\begin{gathered} y=x+3 \\ y=-8+3 \\ y=-5 \end{gathered}[/tex]
Hence, the system of equation has one solution, the solution is ( -8 , -5 )
One Solution ( -8 , -5 )
