📚 Topic Summary
A linear system is a set of two or more linear equations using the same variables. A solution to a linear system is an ordered pair (or triple, etc.) that satisfies every equation in the system. To check if a given point is a solution, simply substitute the $x$ and $y$ values into each equation. If the point makes all equations true, it's a solution! If even one equation is false, it's not a solution. This printable worksheet is designed to help you practice verifying solutions quickly and accurately.
🧠 Part A: Vocabulary
Match each term with its definition:
| Term |
Definition |
| 1. Linear Equation |
a. A set of two or more linear equations. |
| 2. System of Equations |
b. The point(s) where lines intersect. |
| 3. Solution Set |
c. An equation whose graph is a straight line. |
| 4. Ordered Pair |
d. A pair of numbers $(x, y)$ that represents a point on a coordinate plane. |
| 5. Intersection |
e. The set of all solutions to a system of equations. |
✍️ Part B: Fill in the Blanks
To check if an ordered pair is a __________ to a system of equations, you __________ the $x$ and $y$ values into __________ equation. If the ordered pair makes __________ equations true, then it __________ a solution to the system.
🤔 Part C: Critical Thinking
Explain, in your own words, why it's necessary to check a solution in all equations of a linear system, not just one.