system of equation

3. Solution – Occurs when equations have no point in common (parallel lines).
6. Solutions – Occurs when all equations represent the same line.
7. System – A system where all equations are linear (no exponents on variables).
9. System – A system with infinitely many solutions; equations represent the same line.
10. System – A system with exactly one solution; equations intersect at one point.
12. System – A system that has at least one solution.
13. System – A system with no solution; the lines are parallel.

1. of Equations – A set of two or more equations with the same variables.
2. Matrix – A matrix made of just the coefficients of the variables in the system (used in advanced methods like matrix solving).
4. – A method of solving by adding or subtracting equations to eliminate a variable.
5. Pair – A pair of numbers (x, y) that represent a solution in two-variable systems.
8. Point – The point where the graphs of two equations meet; the solution.
11. – A method of solving by plotting equations and finding the intersection point.
14. – The value(s) of the variable(s) that satisfy all equations in the system.
15. – A method of solving by replacing one variable with an expression from another equation.