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

1 Answer
Feb 2, 2017

Answer:

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

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 #x# in terms of #y# or #y# in terms of #x# as follows:

Divide both sides of the equation by #2# to get:

#-3x+y = -4#

Add #3x# to both sides to get:

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

For any value of #x# this gives us the corresponding value of #y#.

This formula is in the form:

#y = mx+c#

known as slope intercept format, where #m=3# is the slope of the line and #c=-4# is the #y# intercept.

If we add #4# to both sides and transpose we get:

#3x = y+4#

Then dividing both sides by #3# we get:

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

For any given #y#, this formula gives us the corresponding value of #x#.

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

#(t, 3t-4)#

where #t in RR#

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]}