# What is the solution of the system of equations: #-6x+2y=-8# ?

##### 1 Answer

#### Explanation:

This system of equations only has one linear equation in two unknowns and hence an infinite number of solutions.

The solutions lie along the line described by the given equation:

#-6x+2y=-8#

We can rearrange this equation to express

Divide both sides of the equation by

#-3x+y = -4#

Add

#color(blue)(y = 3x-4)#

For any value of

This formula is in the form:

#y = mx+c#

known as *slope intercept* format, where

If we add

#3x = y+4#

Then dividing both sides by

#color(blue)(x = 1/3y+4/3)#

For any given

Alternatively, we can use the previous slope intercept format equation to derive a parametric representation of the line as:

#(t, 3t-4)#

where

So we can express the solution space of the original system of equation(s) as:

#color(blue)((x, y) in { (t, 3t-4) : t in RR })#

graph{y=3x-4 [-9.42, 10.58, -5.72, 4.28]}