# How do you solve  5x - y =17, 5x +6y =3 by graphing and classify the system?

Sep 30, 2016

The equations are consistent (see below for method of graphing).

#### Explanation:

For each equation find pairs of values for $\left(x , y\right)$ that satisfy the equation. (If possible, try to find integer values since these will be easier to graph). Find at least 2 pairs for each equation (preferably 3 or more to validate the results)

$\textcolor{red}{5 x - y = 17}$
color(white)("XXX"){: (color(red)(underline(x)),color(red)(underline(y))), (color(red)(4),color(red)(3)), (color(red)(3),color(red)(-2)), (color(red)(5),color(red)(8)) :}

$\textcolor{g r e e n}{5 x + 6 y = 3}$
color(white)("XXX"){: (color(green)(underline(x)),color(green)(underline(y))), (color(green)(3),color(green)(-2)), (color(green)(-3),color(green)(3)), (color(green)(-9),color(green)(8)) :}

Plot each set of points on the Cartesian Plane and draw a line through the point for each set. Since the lines for these equations intersect at a single point $\left(3 , - 2\right)$ the equations are consistent.