[tex]8x + y = -2[/tex]
[tex]4x - y = -14[/tex]
To solve this via the addition method, we just need the two equations together; that means that we will create a new equation where the terms on the left side of both equations are added together and are set equal to the sum of the terms on the right side of both equations:
[tex](8x + y) + (4x - y) = (-2) + (-14)[/tex]
[tex]8x + y + 4x - y = -2 - 14[/tex]
[tex](8x + 4x) + (y - y) = -16[/tex]
[tex]12x + 0 = -16[/tex]
[tex]x = \frac{-16}{12}[/tex]
[tex]x = \frac{-4}{3}[/tex]
Now that we have solved for one term, we can plug this value into either equation to get the value for the other:
[tex]4x - y = -14[/tex]
[tex]4(\frac{-4}{3}) - y = -14[/tex]
[tex]\frac{-16}{3} - y = -14[/tex]
[tex]\frac{-16}{3} + 14 = y[/tex]
[tex]\frac{26}{3} = y[/tex]
This means the solution to the system of equations is [tex](-\frac{4}{3}, \frac{26}{3})[/tex]
