Download Solve using graphing

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.
VOCABULARY
Consistent – has at least 1
solution
Inconsistent – has no solution
Independent – has exactly 1
solution
Dependent – has infinite
solutions (all real numbers)
SOLVING SYSTEMS BY GRAPHING
1.
2.
3.
Solve all equations for y.
Graph all equations on the same
graph.
The lines:
a.
b.
c.
4.
Intersect
Are parallel
Are the same line
Write the solution:
a.
b.
c.
Point of intersection
No solution
All real numbers
EXAMPLES
Solve 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)
EXAMPLES
Solve using substitution:
y=6-x
-x + y = 4
SOLVING SYSTEMS BY ELIMINATION
1.
Determine if you should use:
a.
b.
c.
2.
If
a.
b.
c.
3.
4.
Addition
Subtraction
Multiplication
Addition – add the equations together
Subtraction – subtract the equations
Multiplication – multiply one equation,
then add them together
Substitute your answer back into an
original equation.
Write the solution. (ordered pair, no
solution, or all real numbers)
EXAMPLES
Solve using elimination:
y=6-x
-x + y = 4
CLASSWORK
p. 146
Start with #20 and work
backwards to #11
HOMEWORK
1.
2x + y = -3
6x + 3y = -9
2. 3x – 2y = -1
8y = 5 + 12x
3. 5x + y = 10
4x + y = 4
Solve using your preference:
1. Graphing
2. Substitution
3. Elimination