Answer: They intersect at [tex](2\frac{1}{6}, \frac{1}{3} )[/tex]
Step-by-step explanation:
We can solve this system of equations through elimination
Add (4x+y=9) with (2x-y=4)
[tex]4x+y=9\\+2x-y=4\\=\\6x+0=13[/tex]
Now that y is canceled out we can solve for x
[tex]6x=13\\\frac{6x}{6}=\frac{13}{6} \\x=2\frac{1}{6}[/tex]
Now sub back x into one of the original equations to find the value of y
[tex]4(2\frac{1}{6} )+y=9\\8\frac{2}{3} +y=9\\8\frac{2}{3}-8\frac{2}{3}+y=9-8\frac{2}{3}\\y=\frac{1}{3}[/tex]
