Transcript Warm-Up - Walton High

Warm-Up
8/13/2010
Solve each equation for the indicated variable
1.) 2 x  y  5; y
y  2x  5
2.)  x  2 y  3; x
x  2y 3
3.) 3 x  4 y  12; y
3
y  x3
4
4
x  y4
3
4.) 3 x  4 y  12; x
Any questions over HW?
1.3 Solve Systems of Equations
Algebraically
page 13
System of Equations
Two or more equations with the same variables.
x + y = 11
3x – y = 5
(4, 7) is the unique solution
(4, 7) is a solution to BOTH equations
Ex. 1: Solve by substitution
2x  y  6
3x  4 y  4
So…(4 , -2) is the solution to the system
Solving a System of Equations
Graphing
1) Put each equation in
slope-intercept form
2) Graph
*plot the y-intercept
*use the slope to find
another point
3) Determine the
solution
Substitution
1) Solve one of the
equations for one of the
variables.
2) Substitute into the
other equation
3) Solve
4) Substitute to solve
for the remaining
variable.
Solve the system by substitution
3x  4 y  4
x  2y  2
(-8, 5)
Ex. 3 Solve by elimination (linear
combination)
3x  4 y   1
3x  2 y  0
1 1
 , 
3 2
Solving a System of Equations
Graphing
1) Put each equation in
slope-intercept form
2) Graph
*plot the y-intercept
*use the slope to find
another point
3) Determine the
solution
Substitution
Elimination
1) Solve one of the
equations for one of the
variables.
1) Choose a variable to
eliminate
2) Substitute into the
other equation
2) Make coefficients
opposite numbers by
multiplying
3) Solve
3) Add the equations
4) Substitute to solve
for the remaining
variable.
4) Substitute to solve
for the remaining
variable.
Goal: Find Unique Solutions (ordered pairs)
Ex. 3 solve by elimination
3x  3 y 15
2 x  6 y  22
(2, 3)
Ex. 4 Use elimination to solve
5x + 4y = 11
3x – 5y = -23
Practice Problems
1.) 2y + x = 1
Use substitution
3y – 2x = 12
2.) 5x + 3y = 17
Use elimination
-5x + 2y = 3
3.) 3x + 5y = 30
5x + 3y = 34
Use any method
Homework
Page 161
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#2-12 even
Page 166
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#2-18 even