Step-by-step explanation:
[tex]y = -\frac{2}{3}x + 4[/tex]
[tex]y = \frac{1}{3}x - 2[/tex]
Since both equations are set equal to [tex]y[/tex], we can take the right-hand side of each equation and set them equal to each other to solve for [tex]x[/tex]:
[tex]-\frac{2}{3}x + 4 = \frac{1}{3}x - 2[/tex]
[tex]-\frac{2}{3}x - \frac{1}{3}x = -2 - 4[/tex]
[tex]-x = -6[/tex]
[tex]x = 6[/tex]
Now we can plug this value into either equation to solve for [tex]y[/tex]:
[tex]y = \frac{1}{3}x - 2[/tex]
[tex]y = \frac{1}{3}(6) - 2[/tex]
[tex]y = 2 - 2[/tex]
[tex]y = 0[/tex]
So the solution to the system of equations is [tex](6, 0)[/tex]
