Test Review: Graphing Systems of Equations

Welcome back, class! As we approach our upcoming test, it is time to consolidate everything we have learned about Systems of Equations. This review focuses specifically on solving these systems by graphing.

Remember, a system of linear equations consists of two or more lines. When we solve a system by graphing, we are visually looking for the point of intersection—the specific coordinate pair $(x, y)$ where the lines cross. This point represents the solution that makes both equations true.

Key Steps to Success

As you work through the attached worksheet, follow the process we outlined in the class notes:

  1. Identify Slope and Intercept: Ensure your equation is in Slope-Intercept Form ($y = mx + b$). Identify your slope ($m$) and your y-intercept ($b$).
  2. Graph the First Point: Start by plotting the y-intercept ($b$) on the y-axis.
  3. Move with the Slope: Use the slope as $\frac{rise}{run}$ to map out at least two more points to ensure your line is straight.
  4. Find the Intersection: Repeat the process for the second equation and see where the lines meet.

The Most Important Step: Check Your Work!

If you look at the handwritten notes attached below (specifically Problem 2 and Problem 4), you will see a vital step written in green and blue ink: The Check.

Once you find a potential solution, like $(2, 2)$ from Problem 5, you must plug those numbers back into both original equations to verify.

For example, if your solution is $(x, y)$, substitute those values in: $$ y = mx + b $$ If the left side equals the right side for both equations, you have the correct answer! Use this method to guarantee your grade on the test.

Special Cases

Pay close attention to Problem 3 and Problem 6 in the notes. sometimes you will calculate the slopes and realize they are identical (e.g., $m = \frac{5}{4}$ for both lines). As written in the class notes:

"No point, they're parallel. Same slope... they're not gonna cross."

If the lines are parallel, there is No Solution.

Study Resources

Attached below are the materials you need for this review session:

  • Worksheet: The blank problems for you to practice.
  • Class Notes: My handwritten solutions showing the step-by-step graphing and checking process.

Good luck studying! Practice these problems, check your answers, and you will do great on the test.