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

Aug 8, 2017

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 $x = 0$: $\left(5 \cdot 0\right) - y = 4$

$0 - y = 4$

$- y = 4$

$y = - 4$ or $\left(0 , - 4\right)$

For $x = 2$: $\left(5 \cdot 2\right) - y = 4$

$10 - y = 4$

$- y = - 6$

$y = 6$ or $\left(2 , 6\right)$

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 $x = 0$: $\left(- 2 \cdot 0\right) + 6 y = 4$

$0 + 6 y = 4$

$6 y = 4$

$y = \frac{2}{3}$

For $x = 2$: $\left(- 2 \cdot 2\right) + 6 y = 4$

$- 4 + 6 y = 4$

$6 y = 8$

$y = \frac{4}{3}$

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: $\left(1 , 1\right)$

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