We will look at solving them three different ways: by graphing, by the substitution method, and by the elimination by addition method. In other words, it is where the two graphs intersect, what they have in common.
So if an ordered pair is a solution to one equation, but not the other, then it is NOT a solution to the system.
If your variable drops out and you have a TRUE statement, that means your answer is infinite solutions, which would be the equation of the line.
If you come up with a value for the variable in step 4, that means the two equations have one solution.
Example 4: Solve the equation -2(x - 1) 4y = 5 for y.
Solution: Start by simplifying the left side of the equation. Since you're trying to isolate the y, eliminate every term not containing a y from the left side of the equation.
In other words, add 2x to, and subtract 2 from, both sides of the equation.
Even though that answer is correct, it will make more sense in Graphing Linear Equations if you rewrite it slightly.
If you get an infinite number of solutions for your final answer, is this system consistent or inconsistent? If you get an infinite number of solutions for your final answer, would the equations be dependent or independent? The graph below illustrates a system of two equations and two unknowns that has an infinite number of solutions: Here is the big question, is (3, 1) a solution to the given system?????
Since it was a solution to BOTH equations in the system, then it is a solution to the overall system.