Download Sec 7.1-7.2

Section 7.1
Systems of Linear Equations;
Substitution and Elimination
A movie theater sells tickets for $8.00 each, with
seniors receiving a discount of $2.00. One evening
the theater took in $3580 in revenue. If x represents
the number of tickets sold at $8.00 and y the number
of tickets sold at the discounted price of $6.00, write
an equation that relates these variables.
Suppose we also know that 525 tickets were sold.
Write another equation relating the variables x and y.
2 x  3 y  1
Solve: 
4 x  y  3
2 x  3 y  1
Solve: 
4 x  y  3
2 x  3 y  1
Solve: 
4 x  y  3
Nonlinear Systems
• A nonlinear system of equations is a system in
which at least one of the equations is not linear
equation.
Example:
3x  2 y  5
x  3 y  4
2
Solve the system graphically.
Give the x- and y- coordinates to the nearest hundredth
y
3
x4
x y 6
2
2
Solution: {( -1.68, -1.78), (2.12, -1.24)}
Section 7.2
Linear Systems in Three Variables
Use the method of elimination to solve the system of equations.
2 x  y  z  4

3x  2 y  2 z  10

 x  2 y  3z  7
2 x  3 y  z  0

Solve:  x  2 y  z  5

3x  4 y  z  1
x  y  2z  1

Solve: 2 x  y  z  2
4 x  y  5 z  4
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B)
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