A system of linear equations is a set of two or more linear equations containing the same variables. The solution to a system of linear equations is the set of values that satisfy all equations simultaneously. Graphically, the solution represents the point(s) where the lines intersect. We can solve these systems using various methods like substitution, elimination, or graphing.
Match the terms with their correct definitions:
| Term | Definition |
|---|---|
| 1. Linear Equation | A. A method to solve systems by adding or subtracting equations. |
| 2. System of Equations | B. A straight line on a graph. |
| 3. Solution | C. A set of two or more equations with the same variables. |
| 4. Substitution | D. Values that make all equations in a system true. |
| 5. Elimination | E. A method to solve systems by solving one equation for a variable and substituting it into another. |
Complete the following paragraph with the correct words:
A system of linear equations can have one __________, no __________, or infinitely many __________. We can use the __________ method to solve for one variable in terms of another, then substitute that expression into the other equation. Graphically, the solution is the point of ___________ of the lines.
Explain in your own words why it's important to check your solution when solving a system of linear equations. What could happen if you don't?
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