Question

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

Answer 1

Answer: They intersect at
`(2(1)/(6), (1)/(3) )`

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\\(6x)/(6)=(13)/(6) \\x=2(1)/(6)`

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

`4(2(1)/(6) )+y=9\\8(2)/(3) +y=9\\8(2)/(3)-8(2)/(3)+y=9-8(2)/(3)\\y=(1)/(3)`