Advanced Math / Systems Equations Two Variables
Systems of Equations in Two Variables
Systems of equations in two variables can include linear and nonlinear equations. Common SAT-style systems pair a line with a parabola, a line with a circle-like equation, or a simple nonlinear relation with a linear relation.
Least you need to know
- A solution to a system is an ordered pair that satisfies every equation.
- The number of real solutions can often be determined by the discriminant of the resulting quadratic.
Key notation
- $(x,y)$ — An ordered pair that may solve all equations in a system
Worked example
- Substitute one equation into the other.
- Solve the resulting equation and interpret the coordinate asked for.
Common mistakes
- A system may have two, one, or no real solutions.
- Check whether the question asks for $x$, $y$, or an expression.
How to recognize it
- The system includes at least one nonlinear equation.
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