๐ Topic Summary
Solving systems of equations means finding the values of the variables (usually x and y) that make both equations true at the same time. There are three main methods we use: graphing, substitution, and elimination. Graphing involves plotting the equations and finding where they intersect. Substitution means solving one equation for one variable and plugging it into the other equation. Elimination involves adding or subtracting the equations to get rid of one variable.
The 'most efficient' method depends on the specific equations. If the equations are already set up nicely for a particular method, it's usually best to use that one. Practice helps you quickly recognize which method will be fastest!
๐ง Part A: Vocabulary
Match each term to its definition:
| Term |
Definition |
| 1. System of Equations |
A. A method to solve systems by adding or subtracting equations. |
| 2. Substitution |
B. A method to solve systems by solving for one variable and plugging into the other equation. |
| 3. Elimination |
C. A set of two or more equations with the same variables. |
| 4. Graphing |
D. The point where two lines intersect on a coordinate plane. |
| 5. Solution |
E. A method to solve systems by plotting equations and finding intersections. |
โ๏ธ Part B: Fill in the Blanks
Complete the following paragraph with the correct terms:
When solving a ______ of equations, we are looking for the ______ that satisfies all equations. The ______ method is useful when one equation is easily solved for a variable. The ______ method is useful when the coefficients of one variable are the same or opposites. The ______ method visually represents the equations.
๐ค Part C: Critical Thinking
Explain in your own words when you would choose substitution over elimination, and why.