Lesson 7.2- Substitution, pg. 376

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Presentation transcript:

Lesson 7.2- Substitution, pg. 376 Objectives: To solve systems of equations by using substitution. To solve real-world problems involving systems of equations.

The exact solution of a system of equations can be found by using algebraic methods. One such method is called SUBSTITUTION.

Steps for using SUBSTITUTION Solve one equation for one variable. (Hint: Look for an equation already solved for one of the variables or for a variable with a coefficient of 1.) Substitute into the other equation. Solve this equation to find a value for a variable. Substitute again to find the value of the other variable. Check.

Ex. 1: Solve using substitution. Y = 3x + 2 6x – 2y = -4

2. 4x + y = 12 -2x – 3y = 14

3. 2x + 2y = 8 x + y = -2

You try…. 4. x = 4y 4x – y = 75

5. Y = 3/5x 3x – 5y = 15

Application RESTURANTS The Rodriguez family and the Wong family went to a brunch buffet. The restaurant charges one price for adults ad another price for children. The Rodriguez family has two adults and three children, and their bill was $40.50. The Wong family has three adults and one child, and their bill was $38.00. Determine the price of the buffet for an adult and the price for a child.

2. At the end of the 2000 baseball season, the New York Yankees and the Cincinnati Reds had won a total of 31 World Series. The Yankees had won 5.2 times as many World Series as the Reds. How many World Series did each team win?

3. The base of the triangle is 4 inches longer than the length of one of the other sides. Use a system of equations to find the length of each side of the triangle. Perimeter = 46 inches x inches x inches y inches

Summary 3 types of solutions to a linear system One solution No solution- two sides of an equation are not equal Many solutions-two sides of an equation are equal NBA #14, pg. 379, problems 12-32 even