Systems of Equations — Word Problems
SAT Skill: Translating real-world scenarios into two (or more) equations, then solving the system to find the answer. This is one of the most frequently tested algebra topics on the SAT Math section.
1. What Is a System of Equations?
A system of equations is a set of two or more equations that share the same unknowns. A solution to the system is a set of values that makes every equation true simultaneously.
General form (two variables):
$$\begin{cases} a_1 x + b_1 y = c_1 \\ a_2 x + b_2 y = c_2 \end{cases}$$
The solution $(x, y)$ is the point where the two lines intersect.
Interactive: Visualizing a System of Two Linear Equations
Interactive visualization — available in the full lesson
The blue line represents $x + y = 14$ and the pink line represents $3x + 2y = 30$. They intersect at $(2, 12)$.