Concept 2

Solve systems of linear equations (substitution/elimination) and interpret intersections.

Use substitution or elimination to find the point where both equations are true.

Core Idea

The solution to a system is the point that makes both equations true at the same time. Use substitution or elimination based on which one clears the system faster.

Understanding

Rule: Substitution is efficient when one equation is already solved for a variable. Elimination is efficient when coefficients line up with a quick add or subtract.

If the system comes from a graph or a context, the solution is the intersection. That point is not just two numbers; it represents the shared value where both relationships agree.

Step by Step

Choose substitution when one equation is already solved for a variable.
Choose elimination when the coefficients are easy to add or subtract away.
Interpret the solution as the intersection point.

Misconceptions

Solving only one equation and stopping too early.
Forgetting to check that the ordered pair satisfies both equations.
Using the wrong method when a faster one is available.

Question

Worked Example

What is the solution to the system $𝑦 = 3 𝑥 - 2$ and $𝑦 = 𝑥 + 6$ ?

Select an answer to see the explanation