let w = width let l = length width width length 2. If the perimeter is 38 m, find the dimensions. g + b = 25 2g = 3b There are 15 girls and 10 boys in the class.ħ Example 2 The length of a rectangle is 4 m more than twice its widthĮxample 2 The length of a rectangle is 4 m more than twice its width. Let g = # of girls Let b = # of boys Write an equation for each of the first two sentences. Choose a different variable for each type of person. How many boys and girls are there in the class? Assign Labels. Twice the number of girls is equal to 3 times the number of boys. = length let l = length let w = width width width length Formula The width is 18 m and the length is 37 m.Ħ Example 1 A class has a total of 25 studentsĮxample 1 A class has a total of 25 students. If the perimeter is 110 m, find the dimensions.
The length of a rectangle is 1 m more than twice its width. Jose is 3 and Meg is 15.ĥ The length of a rectangle is 1 m more than twice its width m = 5j m + j = 18 Solve the system of equations. Let m = Meg’s age Let j = Jose’s age Write an equation for each of the first two sentences. Choose a different variable for each person. 5) Write a sentence and check your solution in the word problem.Ĥ Meg’s age is 5 times Jose’s age. (Translate from sentences) 3) Write two algebraic models (equations). Elimination Using Multiplication –can be applied to create opposites in any system.ģ Solving Word Problems Using A Linear Systemġ) Write two sets of labels, if necessary (one set for number, one set for value, weight etc.) 2) Write two verbal models. Elimination Using Subtraction –convenient if one of the variables has the same coefficient in the two equations. Elimination Using Addition –convenient when a variable appears in different equations with coefficients that are opposites. It is especially convenient when one of the variables has a coefficient of 1 or –1. Substitution – requires that one of the variables be isolated on one side of the equation. Graphing – can provide a useful method for estimating a solution and to provide a visual model of the problem. Presentation on theme: "Linear Systems and Problem Solving"- Presentation transcript:Ģ Ways to Solve a System of Linear Equations
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