SOLUTION: I need to classify the system as consistent or inconsistent, and dependent or independent. x + y = 8 x-y=4

Question 737500: I need to classify the system as consistent or inconsistent, and dependent or independent.
x + y = 8
x-y=4
Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!

Solved by pluggable solver: Solve the System of Equations by Graphing

Start with the given system of equations:

In order to graph these equations, we need to solve for y for each equation.

So let's solve for y on the first equation

Start with the given equation

Subtract from both sides

Rearrange the equation

Divide both sides by

Break up the fraction

Reduce

Now lets graph (note: if you need help with graphing, check out this solver)

Graph of

So let's solve for y on the second equation

Start with the given equation

Subtract from both sides

Rearrange the equation

Divide both sides by

Break up the fraction

Reduce

Now lets add the graph of to our first plot to get:

Graph of (red) and (green)

From the graph, we can see that the two lines intersect at the point (,) (note: you might have to adjust the window to see the intersection)

we usually use the word "consistent" when we are more interested in
indicating that the system does HAVE a solution, rather than
indicating how many solutions it has
"Inconsistent" means no solution,
"Independent" and "Dependent" BOTH mean there a solution
since your system has solution (one intersection point), it is "Independent" or "Dependent"
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