Systems of Equations

System of Equations

• two (or more) linear equations
• with two (or more) variables
• solution(s) values for x and y
• satisfy both equations

Untitled Slide

• How many solutions are there?
• Single linear equation?
• Two linear equations?
• graphing

Number of Solutions

• one - lines intersect one
• infinite - same line described
• none - parallel lines

Quick Tests for # of Solutions

• different slopes - 
• same slopes - 
• y-intercepts - 

Methods

• Substitution
• Elimination
• Graphing

Substitution

• Solve one equation for one variable in terms of the other.
• Prefer a variable with a coefficient of one.
• Substitute the equivalent expression for the variable.
• Solve the single variable equation created.
• Substitute numeric value for variable into expression.

Examples

Elimination

• inverse coefficients
• add the equations together
• match variables and constants

Examples

Graphing

• inexact except on computer
• visual
• graph both lines
• intersection is the solution

Examples

How could you "hack" the systems of equations portion of a multiple choice test?

Hack

• substitute answer choices into the equations
• the choice that works - right answer
• advantage: nearly certain to get correct answer
• disadvantage: slower than other methods

Quick Hack

• graph lines
• sketch or use graphing calculator
• choose most reasonable answer
• advantage: quick
• disadvantage: inexact

Other Hacks?