Preparing the System
To use elimination, you must ensure that these are lined up vertically.
What are Like Terms (or Variables/Constants)?
Add these: (x2+2x) and (−x2+5x).
What is 7x?
Solve for x: x2−25=0.
Answer:What are 5 and -5.
Once you find x=2, you do this to find the value of y.
Answer: What is Substitution?
If Equation A has y and Equation B has y, you should do this operation to eliminate them.
What is Subtraction?
When eliminating y in the system {y=x2+10,y=5x}, this is the resulting single equation.
What is 0=x2−5x+10?
Solve by factoring: x2−5x+6=0.
What are 2 and 3?
If y=x2 and you found x=3 and x=−3, these are the two y-values.
What is 9 (for both)?
If you have 3x2 in one equation and x2 in the other, you must multiply the second equation by this number to eliminate the x2 term by adding.
What is -3?
You eliminate y and are left with x2−9=0. These are the two values for x.
What are 3 and −3?
In the equation 2x2+8x=0, you should factor out this "Greatest" thing first.
What is the GCF (Greatest Common Factor, which is 2x)?
A solution to a quadratic system represents this specific spot on a graph.
What is the Intersection Point?
True or False: You can eliminate the x2 term even if one equation is in Standard Form and the other is in Vertex Form.
What is False? (You must convert them to the same form first)
After eliminating a variable, you are left with a quadratic that cannot be factored. You should use this famous formula.
What is the Quadratic Formula?
Solve: x2+10x+25=0.
What is −5?
If you have two x-values and two y-values, you should write your final answer in this format.
What are Ordered Pairs (x,y)?
The mathematical term for a number placed in front of a variable, like the 4 in 4x2.
What is a Coefficient?
If adding two equations results in 0=12, the system has this many solutions.
What is Zero (No Solution)?
If your eliminated equation is x2=−16, the solutions are in this number system.
What are Imaginary/Complex numbers?
If the system is two identical parabolas, it has this many solutions.
What is Infinitely Many?