Solving Linear Systems Algebraically with Substitution Section 3-2 Pages 160-1-67.

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Presentation transcript:

Solving Linear Systems Algebraically with Substitution Section 3-2 Pages

Objectives I can use the substitution method to solve equations I can solve word problems using Substitution

Substitution Method Goal 1. Isolate one variable in one equation 2. Substitute into the other equation(s) AWAYS pick the easiest equation to isolate.

Which Equation to Isolate

Example 1

What does it mean? When we found the solution (6, -1) What does that really mean??? Intersection of the 2 graphs!!

y=-2/5x+7/5 y=-1/4x+1/2 (6, -1)

Example 2

Your Turn Solve the following system of equations using substitution:

Other Methods Remember, the solution to a system of equations if an Ordered Pair You know 2 other methods to check your answers: –Graphing to find the intersection –Graphing Calculator and asking for the intersection (2 nd, Trace, Intersection, E, E, E)

Solution Types Remember there are 3 types of solutions possible from a system of equations!

No Solution vs Infinite How will you know if you have No Solution or Infinite Solutions when solving by Substitution??

Remember Back to Solving Equations No Solution Variables are gone and you get this: 2x + 3 = 2x – 4 3 = -4 This is not possible, so No Solution Infinite Solutions Variables are gone and you get this: 2x + 3 = 2x = 3 This is always true, so Infinite Solutions

Word Problems When solving a word problem, consider these suggestions 1. Identify what the variables are in the problem 2. Write equations that would represent the word problem, looking for key words Sum, difference, twice, product, half, etc…

Example 1 GEOMETRY: The length of a rectangle is 3 cm more than twice the width. If the perimeter is 84 cm, find the dimensions. Variables: Length (L) Width (W) Equations: L = 2W + 3 2L + 2W = 84 Now, solve by substitution

Example 2 Melissa has 57 coins in dimes and nickels. The total value of the coins is $4.60. How many coins of each kind does she have? Nickels (N) Dimes (D) Equations: N + D = 57 10D + 5N = 460 Now, solve by substitution

Example 3 At a recent movie, adult tickets were $4.50 and student tickets were $2.50. During opening night a total of 300 tickets were sold earning $1130. How many of each ticket type were sold? Adult Ticket (A) Student Ticket (S) Equations: A + S = A S = 1130 Now, solve by substitution

Homework Substitution Worksheet