Algebra / Systems Linear Equations
Systems from Contexts and Graphs
A system of linear equations can model two simultaneous conditions. Graphically, the solution is the intersection point of the two lines.
Least you need to know
- A solution to a system satisfies both equations.
- Parallel lines have no solution.
- Equivalent equations have infinitely many solutions.
Key notation
- $\begin{cases}x+y=20\3x+5y=76\end{cases}$ — A system that can model a total number and a total cost
Worked example
- If $x+y=10$ and $2x+y=13$, subtract the first equation from the second.
- This gives $x=3$.
- Then $y=7$.
Common mistakes
- Use both equations before interpreting the answer.
- A graph intersection gives both the $x$- and $y$-coordinates of the solution.
How to recognize it
- The problem describes two quantities and two conditions.
- The problem asks where two linear graphs intersect.
- The problem asks for no solution or infinitely many solutions.
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