Identifying and verifying a solution to a system | Grade 8 (TX TEKS) | Khan Academy

Introduction

In this tutorial, we will explore how to identify and verify a solution to a system of two linear equations using a graph. This process is crucial in understanding how different equations interact and where they intersect, which represents the solution to the system. Whether you're preparing for a test or just looking to reinforce your understanding, this guide will break down the steps clearly.

Step 1: Identify the Graphs of the Equations

• Start by reviewing the equations provided. For this tutorial, we have:
  • Equation 1: y = -2x - 2 (represented in blue)
  • Equation 2: y = -1/4x + 5 (represented in brown)
• Plot both equations on a coordinate grid:
  • For the first equation, find points by substituting values for x and calculating y.
  • For the second equation, do the same.
• Observe where the two lines intersect. This point of intersection represents the solution to the system.

Step 2: Estimate the Intersection Point

• Visually inspect the graph to estimate the coordinates of the intersection point.
• For example, it appears that the intersection occurs at x = -4 and y = 6.
• Write down this estimated solution as a coordinate pair: (-4, 6).

Step 3: Verify the Solution

To verify that the point (-4, 6) is indeed a solution for both equations, substitute x = -4 into each equation and check if y equals 6.

Verification for Equation 1

1. Substitute x into the equation:
   • y = -2 * (-4) - 2
2. Calculate:
   • y = 8 - 2 = 6
3. Since the result matches y = 6, the point satisfies Equation 1.

Verification for Equation 2

1. Substitute x into the second equation:
   • y = -1/4 * (-4) + 5
2. Calculate:
   • y = 1 + 5 = 6
3. Again, the result matches y = 6, confirming that the point satisfies Equation 2.

Conclusion

You have now successfully identified and verified a solution to a system of linear equations using a graphical approach. The intersection point (-4, 6) was confirmed to satisfy both equations. This method can be applied to any system of linear equations, enhancing your problem-solving skills in algebra. For further practice, try identifying solutions from different systems of equations or explore other related topics on Khan Academy.