Solving systems of equations
There are THREE (3) types of solutions when it comes to solving systems of equations. Either you will get:
- One solution (which will be given in an ordered pair) - This is when the two lines cross each other in ONE place. Where they cross is the answer. Write it in an ordered pair (x,y).
- No solution - This is when the two lines are parallel to each other and never cross. If they never cross then there will never be an intersection point; hence No Solution
- Infinite solutions - This is when the two lines are directly on top of each other. Since there are infinite points where the two lines cross, that is why there are infinite solutions.
How do you find the answer?
Systems of equations can be solved by:
- Graphing Method
- Substitution Method
- Elimination Method
- Matrix Method / Cramer's Rule
We will be using #1 - Graphing Method!!
- Graph both lines on the SAME coordinate plane. Pay careful attention to your BEGIN, RISE, FALL, & RUN RIGHT.
- Make your lines perfectly straight following the RISE/FALL/RUN numerous times until you have a longer line.
- Look at graph.
- Do they cross each other at ONE place? Then you have ONE SOLUTION. Your answer is the ordered pair (x,y) where they cross. The coordinates of the intersection point is your answer.
- Are they parallel? Then you have NO SOLUTION. Write no solution.
- Are they they exact same line? Then you have INFINITE solutions. Write infinite.