Concept 2

Interpret the solution as the intersection point of two lines.

The solution to a system is the point where the two lines intersect.

Core Idea

The solution to a system of two linear equations is the point where the two lines intersect on the coordinate plane.

Understanding

The solution is the intersection point. Every point on a line satisfies that line's equation; the solution to a system is the point that satisfies both.

Solve algebraically and get a coordinate pair, or read the intersection from the graph.
That pair must work in both equations.
If a point works in only one equation, it is not the solution.

Misconceptions

Confusing the $𝑥$ -intercept or $𝑦$ -intercept of a single line with the intersection of two lines.
Reading the intersection from a graph but swapping $𝑥$ and $𝑦$ — reporting $(1, 3)$ instead of $(3, 1)$ .

Question

Worked Example

Line $𝑝$ is defined by $𝑦 = 2 𝑥 - 1$ and line $𝑞$ is defined by $𝑦 = - 𝑥 + 5$ . At what point do lines $𝑝$ and $𝑞$ intersect?

Select an answer to see the explanation