Question

Explain how you can determine the following system has one unique solution- with out actually solving it 2x+y=42y=6-2x

Answer 1

To answer this, both equations must be in slope-intercept form:

y=mx+b

Where m is the slope.

If both slopes are different, there is one solution:

Solve for y :

• 2x+y=4

y=-2x-4

• 2y=6-2x​

y= (6-2x)/2

y= 3-x

y= -x+3

So the system is:

y=-2x-4

y= -x+3

Slopes are :

m1=-2 ; m2= -1

Both slopes are different, so, the system has one unique solution.