Solve by Substitution.notebook
August 25, 2016
Warm Up
1. Solve: 2. State the direction of opening for the function
y = 3. State the vertex of each absolute value function.
y = 4. Describe the transformations.
y = Warm Up
SYSTEM OF EQUATIONS
Two or more equations in the same variables
A solution of a system of equations is any ordered pair that satisfies both equations.
EXAMPLE: Is (5,2) a solution of the system?
There are 3 methods to solve systems of equations:
1. Graphing
2. Substitution
3. Elimination (Linear Combination)
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Solve by Substitution.notebook
August 25, 2016
Possible Solutions to System of 2 Linear Equations
Case #1: ONE solution
Case #2: NO solution
Case #3: INFINITE solutions
Possible solns graphically
Graph each system. Then find the solution from the graph.
1.
x + 2y = ­8
y = x + 4
2. y = ­2x + 4
­4x ­ 2y = ­8
Solve by Graphing
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Solve by Substitution.notebook
August 25, 2016
Graph each system. Then find the solution from the graph.
3.
­x + y = 7
2x ­ 2y = ­18
4.
4x ­ 3y = ­15
x + 2y = ­ 1
Solve by Graphing
USING SUBSTITUTION TO SOLVE LINEAR SYSTEMS
Use substitution to solve a system of equations when:
a. one of the equations reads as y = or x =.
b. one of the equations can be quickly changed to y = or x =.
In general, solve for the variable whose coefficient is 1.
Example:
Steps: 1. Solve an equation for one of its
variables.
2: Plug your equation from step 1
into the equation you did not use.
3: Solve for the remaining variable.
4: Put the answer from Step 3 into one of the original equations.
Solve By Substitution
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Solve by Substitution.notebook
August 25, 2016
EXAMPLES:
3. 2x + 4y = 42
3x + y = 8
2.
Solve By Substitution
5. y = -x + 2
y = 2x - 1
4.
Solve By Substitution
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Solve by Substitution.notebook
August 25, 2016
5.
6.
Infinite and No Solutions
When solving a system of 2 linear equations algebraically, we STILL have three possible solutions.
ONE solution
one ordered pair, which is the point of intersection for the 2 lines
NO solution
a false statement, like 0 = #, which means the lines are parallel and never intersect
INFINITE
solutions
a true statement, like 0 = 0, which means the lines are the same line and every point on the line is a solution to the system
Possible Solutions Algebraically
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Solve by Substitution.notebook
August 25, 2016
USING LINEAR COMBINATION (ELIMINATION) TO SOLVE LINEAR SYSTEMS
Use elimination to solve a system of equations when:
a. one of the variables in the equations has opposite coefficients.
b. the equations can be multiplied so that one of the variables has opposite coefficients.
Example:
Step 1: Multiply one or both equations by a number, so the coefficients of either x or y are opposites. Step 2: Add the equations together and solve.
Step 3: Substitute your answer from step 2
into one of the equations and solve for the other variable.
*Write your final answer as a point.
Solve by Elimination
7.
8.
Solve By Elimination 6