Systems of Equations in Two and Three Variables

What is the name of this unit?

• System of equations & Equations with no common coefficients.

• Multiplying coefficients

• Adding variables

• Adding & multiplying variables with coefficients.

Solve the system of equations.

• (10, 3)

• (6, 3)

• (15, 3)

• No solution

• Infinite Solution

A __________ is a set of two or more equations. A system of equations means finding the __________ where the two lines intersect, or the one solution (x, y) that makes both equations true. There are three ways to solve: substitution, elimination, and equal values.

• System of Equations

• solving

• coordinate pair

• slope

• Slope-Intercept From (y=mx+b)

__________ works best when both equations are equal to the same variable. Substitution works best when one equation is equal to __________ variable. Elimination works well when both equations are in __________ form.

• Elimination

• Standard Form (Ax+By=C)

• Slope-Intercept Form (y=mx+b)

• one

• Equal Values

To solve a system by Equal Values, set both __________ to each other. Solve the equation for __________ variable. Substitute the value you got back into one of the original equations to solve for the second variable. List your solution as a __________ (x, y).

• two

• equations

• coordinate pair

• one

• variables

Solve for y.

Solve for y

• Infinite Number of Solutions

• No Solution

• One Solution

• Two Solutions

• Not possible

• Graphing

• Substitution

• Elimination

• None

• Equal Values