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Math 101 Review sheet

Math 101 Review sheet - Intermediate Algebra Exam 1 Review...

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Intermediate Algebra Exam 1 Review 5.5 Solving linear systems of two equations by graphing Be able to find either: x-intercept and y-intercept for each of the equations. Or be able to find the slope- intercept, y = mx + b, equation of the line for each equation in the system. In the example, the two lines cross at the ordered pair (- 1,1) which is the solution. Additionally, be able to verify an ordered pair as a solution to a system of equations. Example: + = 2x 3y 1 - =- 4x 3y 7 Solving linear systems of two equations by substitution From p. 235 in the text. Step 1: Solve one of the equations for one variable in terms of the other variable if neither equation is in such a form. (If possible, make a choice that will avoid fractions.) Step 2: Substitute the expression obtained in step 1 into the other equation. This produces an equation in one variable. Step 3: Solve the equation obtained in step 2. (2x+3y=1) (4x-3y=-7) 2x+3y=1 subtract 2x from both sides -2x -2x 3y = -2x + 1 divide both sides by 3 /3 /3 /3 =- + y 23x 13 y is now isolated. - 4x 3 - + 23x 13 =- 7 4x + 2x -1 = -7 distribute the - 3 6x -1 = -7 combine like terms 6x = -6 add 1 to both sides
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5.5 Solving linear systems of two equations by graphing Be able to find either: x-intercept and y-intercept for each of the equations. Or be able to find the slope- intercept, y = mx + b, equation of the line for each equation in the system. In the example, the two lines cross at the ordered pair (- 1,1) which is the solution. Additionally, be able to verify an ordered pair as a solution to a system of equations. Example: + = 2x 3y 1 - =- 4x 3y 7 Step 4: Use the solution obtained in step 3, along with the expression obtained in step 1, to determine the solution of system. x = -1 divide both sides by 6 2 (-1) +3y = 1 -2 – 3y = 1 -3y = -3 y = 1 Using systems of equations to solve word problems— investment problems, sales problem, and purchasing problem You should expect one of each type of problem on the exam. Problems worth looking at in the Homework Section 9, 19, 27, 41, 45, 47, 49, 51, 53, 54, 55, 57 5.6 Solving linear systems by the elimination-by-addition method Using systems of equations to solve word problems— mixture problems, purchasing problems Practice—6, 14, 18, 22, 25, 34, 36, 40, 50 On My Own—8, 10, 24, 38, 10x - 8y = -11 8x + 4y = 8 1. Choose to add a variable to 0.
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