Math 1 · Unit 6 · Lesson 1 · part 2 of 5
Two equations at once
Until now every problem had one equation.
Two equations at once
Until now every problem had one equation. A system of equations is two or more equations that all have to be true at the same time. Here is one:
y = 2x − 1 and y = −x + 5
Each equation on its own is a line with every point on it a solution (Unit 3). A solution of the system is a point that works in both: the same x and the same y make both sentences true. On the graph, that is the one place the two lines share a point: where they cross, the intersection.
It has to work in every equation. (0, −1) is on the first line but not the second, so it is not a solution of the system. (2, 3) is on both. Check: 2 × 2 − 1 = 3, and −2 + 5 = 3. Both true. Say it every time: a solution of a system works in every equation, or it is not a solution.