Question

Where do 2x - y = 4 and 4x + y = 9 intersect?

Answer 1

Answer: They intersect at $(2\frac{1}{6}, \frac{1}{3} )$

Step-by-step explanation:

We can solve this system of equations through elimination

Add (4x+y=9) with (2x-y=4)

$4x+y=9\\+2x-y=4\\=\\6x+0=13$

Now that y is canceled out we can solve for x

$6x=13\\\frac{6x}{6}=\frac{13}{6} \\x=2\frac{1}{6}$

Now sub back x into one of the original equations to find the value of y

$4(2\frac{1}{6} )+y=9\\8\frac{2}{3} +y=9\\8\frac{2}{3}-8\frac{2}{3}+y=9-8\frac{2}{3}\\y=\frac{1}{3}$