Question

How do you solve the system of equations by graphing and then classify the system as consistent or inconsistent `x+y = 16` and `x-y = -2`?

Answer 1

Draw the straight line graphs and find the point of intersection.
`x=7 and y=9`
There is one solution, so the system is consistent.

Explanation:

Each of these equations represents a straight line.

If we draw the two lines, the point of intersection represents the simultaneous solution of the two equations.

Change each equation into 'slope-intercept form' to make the graphing easier:

A consistent system means that there is at least one solution to the equations, which is what we have here. But there is only one point of intersection, it is an independent solution.

`y = -x+16 " and " y = x+2`
graph{(y+x-16)(y-x-2)=0 [-3.495, 16.505, 1.24, 11.24]}

If the two lines were parallel they would not intersect at all and the system would be inconsistent.