Algebra / Linear Equations Two Variables
Linear Equations in Two Variables
A linear equation in two variables can be written in forms such as $ax+by=c$ or $y=mx+b$. A solution is an ordered pair $(x,y)$ that makes the equation true.
Least you need to know
- An ordered pair is a solution if substituting its coordinates makes the equation true.
- The $x$-intercept occurs when $y=0$; the $y$-intercept occurs when $x=0$.
Key notation
- $(x,y)$ — An ordered pair whose first coordinate is $x$ and second coordinate is $y$
Worked example
- Substitute the known coordinate into the equation.
- Solve for the missing coordinate.
Common mistakes
- In $(x,y)$, the first coordinate is $x$.
- For the $x$-intercept, set $y=0$.
How to recognize it
- The equation contains two variables.
- The problem may ask for an intercept or missing coordinate.
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