Question

How do you solve the system `5x-y=4` and `-2x+6y=4` by graphing?

Answer 1

See a solution process below:

Explanation:

First, solve for two points on the first line, plot the points and draw a line through the points:

For `x = 0`: `(5 * 0) - y = 4`

`0 - y = 4`

`-y = 4`

`y = -4` or `(0, -4)`

For `x = 2`: `(5 * 2) - y = 4`

`10 - y = 4`

`-y = -6`

`y = 6` or `(2, 6)`

graph{(5x - y - 4)(x^2 + (y + 4)^2 - 0.125)((x-2)^2 + (y - 6)^2 - 0.125) = 0 [-20, 20, -10, 10]]}

Do the same for the second equation:

For `x = 0`: `(-2 * 0) + 6y = 4`

`0 + 6y = 4`

`6y = 4`

`y = 2/3`

For `x = 2`: `(-2 * 2) + 6y = 4`

`-4 + 6y = 4`

`6y = 8`

`y = 4/3`

graph{(-2x + 6y - 4)(x^2+(y - (2/3))^2-0.125)((x-2)^2+(y - (4/3))^2-0.125) (5x - y - 4)(x^2 + (y + 4)^2 - 0.125)((x-2)^2 + (y - 6)^2 - 0.125) = 0 [-20, 20, -10, 10]]}

Zooming in, we can see the lines intersect at: `(1, 1)`

graph{(-2x + 6y - 4)(5x - y - 4)((x -1)^2+(y-1)^2-0.0125) = 0 [-6, 6, -3, 3]}