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WHAT IS A SYSTEM OF LINEAR EQUATIONS?

• A system of linear equations is 2 or more equations with the same variables.

• To solve a system of equations, you must find the ordered pair that satisfies all of the equations.

VOCABULARYConsistent – has at least 1

solutionInconsistent – has no solutionIndependent – has exactly 1

solutionDependent – has infinite

solutions (all real numbers)

SOLVING SYSTEMS BY GRAPHING

1. Solve all equations for y.

2. Graph all equations on the same graph.

3. The lines:a. Intersectb. Are parallelc. Are the same line

4. Write the solution:a. Point of intersectionb. No solutionc. All real numbers

EXAMPLESSolve using graphing:

y = 6 - x

-x + y = 4

SOLVING SYSTEMS BY SUBSTITUTION

1. Solve for one variable.

2. Substitute your solution into a different equation.

3. Solve for the second variable.

4. Substitute your answer back into your equation in number 1.

5. Write the solution. (ordered pair, no solution, or all real numbers)

EXAMPLESSolve using substitution:

y = 6 - x

-x + y = 4

SOLVING SYSTEMS BY ELIMINATION1. Determine if you should use:

a. Additionb. Subtractionc. Multiplication

2. Ifa. Addition – add the equations togetherb. Subtraction – subtract the equationsc. Multiplication – multiply one equation, then

add them together

3. Substitute your answer back into an original equation.

4. Write the solution. (ordered pair, no solution, or all real numbers)

EXAMPLESSolve using elimination:

y = 6 - x

-x + y = 4

CLASSWORK

p. 146 Start with #20 and work

backwards to #11

HOMEWORK1. 2x + y = -3

6x + 3y = -9

2. 3x – 2y = -1

8y = 5 + 12x

3. 5x + y = 10

4x + y = 4

Solve using your preference:

4. Graphing

5. Substitution

6. Elimination