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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 x4 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 A) B) A) B) C) D)