warm up 1)find the 43 rd term of the sequence 47, 34, 21, 8, …. 2)rewrite in slope-intercept form...
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Warm Up
1) Find the 43rd term of the sequence 47, 34, 21, 8, ….
2) Rewrite in slope-intercept form -5y + 3x = -9
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Homework CheckPage 21a) t = 14c – 4 b) $803a) c = .02n + .30 b) 740 minutes
Page 31)a)4.29x + 3.99y = 30 b) 5.1 pounds4) a) 2x + 5y = 150 b) (0,30) (75,0)
(50,10)
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Homework Check 2.2 (Page 4) 1) y = 4/3x – 8 2) y = 1/2x – 7
3) a)2 b) 3 c) 1 d) 4
4) a) y = .75x + 3 b) $9c) 16 miles
5) a) 2W + 1T = 20 b) 6 tie games
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Systems of Equations
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OBJECTIVES• To understand what a system of
equations is. • Be able to solve a system of
equations from graphing, substitution, or elimination
• Determine whether the system has one solution, no solution, or an infinite amount of solutions.
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Defining a System of Equations
• A system of equations is a grouping of 2 or more equations, containing one or more variables.
Examples:
x + y = 2
2x + y = 5
2y = x + 2
y = 5x - 7
6x - y = 5
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Solution?
To be a solution to the system, all equations must be satisfied.
Is (-3, 4) a solution to the system?
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Types of SolutionsIntersecting Lines have ONE unique solution.
Coincidental Lines (or same lines) have infinitely MANY solutions.
Parallel Lines have NO solutions!
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Solving Systems of Equations
• There are three methods to solving a system of equations
1. Graphing2. Substitution3. Elimination
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Graphing
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Graphing CalculatorStep 1:
Step 2:
Step 3:
Step 4:
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Examples…
1)
Determine whether the following have one, none, or infinitely many solutions
2y + x = 8
y = 2x + 4
3) 2) x - 5y = 10
-5y = -x +6
y = -6x + 8
y + 6x = 8
ANS: One Solution
ANS: No Solution
ANS: Infinite Solutions
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Solving Systems by Substitution
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Solving by Substitution Steps
If one of the equations is already solved for a variable, Substitution may be an easy method to solve.
Step 1: Make sure one of the equations is solved for a variable.
Step 2: Substitute the expression into the other equation.
Step 3: Solve for the variable.
Step 4: Substitute the value of x (or y) into either equation and solve.
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ExampleSolve the system by substitution.
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Solving Systems by Elimination
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Elimination
We can solve by elimination by either Adding or Subtracting two equations to eliminate a variable!
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Example
Solve by Elimination
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Example
Solve by Elimination
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More with Elimination
If one will not cancel, multiply one or both equations to get variables to cancel
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Example
Solve the system by elimination.
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Special Solutions
Solve each system by elimination.
1. 2.
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Homework