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Math 101 Review sheet

# Math 101 Review sheet - I ntermediate 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:

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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. Step 4: Use the solution obtained in step 3, along with the expression obtained in step 1, to determine the solution of system. (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 is now isolated. 4x + 2x -1 = -7 distribute the -3 6x -1 = -7 combine like terms 6x = -6 add 1 to both sides 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.

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