SYSTEMS OF LINEAR EQUATIONSSUBSTITUTION AND ELIMINATION

Objectives:

Solve Systems of Equations by Substitution and Elimination

Identify Inconsistent Systems of Equations containing two or three variables

Solve Systems of Equations containing two or three variables

Systems of Linear Equations• A collection of two or more linear equations in the form

that are straight lines when graphed, each containing one or more variables with no exponents other than 1

• Solution of a System of Linear Equations in two variables: an ordered pair that satisfies both equations in the system

• A system of linear equations can have exactly one solution (Consistent), no solution (Inconsistent) or infinitely many solutions. The lines either intersect at one point, are parallel or are identical.

Ax By C

Methods to solve systems of equations

• Graphing: graph both of the equations in the same rectangular coordinate system. Find the solution to the linear system by locating the point

• Substitution: solve either of the equations for one variable in terms of the other, substitute the expression into the other equation, solve for that variable and the other variable

• Elimination: rewrite both equations in the form , multiply either equation or both equations by appropriate nonzero numbers so that the sum of one of the coordinates coefficients is 0, add the equations and solve for the variable and the other variable

Ax By C

EX: Solve the system of equations

• 1. • 2.5 13

2 3 12

x y

x y

3 6 2

5 4 1

x y

x y

EX: Solve the system of equations

• 3. • 4.2 1

4 2 3

x y

x y

3 2

15 5 10

y x

x y

EX: Solve the system of equations

• 5. 2 3 7

2 4

3 2 2 10

x y z

x y z

x y z