Algebra II (Cliffs Quick Review) by Edward Kohn, David Alan Herzog

By Edward Kohn, David Alan Herzog

By way of pinpointing the belongings you really want to grasp, not anyone does it larger than CliffsNotes. This speedy, potent educational is helping you grasp middle algebraic suggestions -- from linear equations, family and features, and rational expressions to radicals, quadratic structures, and factoring polynomials -- and get the very best grade.
At CliffsNotes, we're devoted to assisting you do your top, regardless of how demanding the topic. Our authors are veteran academics and gifted writers who know the way to chop to the chase -- and nil in at the crucial info you must prevail.

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Both are treated extensively in this chapter. This chapter also explores Cramer’s rule — the application of determinant solution to equations. Linear Equations: Solutions Using Elimination To use elimination to solve a system of three equations with three variables, follow this procedure: 1. Write all the equations in standard form cleared of decimals or fractions. 2. Choose a variable to eliminate; then choose any two of the three equations and eliminate the chosen variable. 3. Select a different set of two equations and eliminate the same variable as in Step 2.

To do this, multiply the top equation by 2 and the bottom equation by 5. multiply (2) 4x + 10y = 6 multiply (5) 15x - 10y = 5 2x + 5y = 3 3x - 2y = 1 Add the new equations, eliminating y. 4x + 10y = 6 15x - 10y = 5 19x = 11 Solve for the remaining variable. F 46 4/25/01 8:40 AM Page 46 CliffsQuickReview Algebra II Repeat Steps 2 through 4 (using new multiplication factors) to eliminate x and solve for y or substitute the above value for x and solve for y. Method 1: Eliminate x and solve for y. 6x + 15y = 9 multiply (3) 2x + 5y = 3 - 6x + 4y =- 2 multiply (- 2) 3x - 2y = 1 19y = 7 y = 197 Method 2: Substitute for x and solve for y.

Example 10: Find the equation of the line containing the points (–3, 4) and (7, 2) and write the equation in both point-slope form and standard form. For the point-slope form, first find the slope, m. y - y1 x - x1 = m m= 2-4 7 - ^ - 3h = - 102 = - 15 Now, choose either given point, say (–3, 4), and substitute the x and y values into the point-slope form. F 34 4/19/01 8:50 AM Page 34 CliffsQuickReview Algebra II For the standard form, begin with the point-slope form and clear it of fractions by multiplying both sides by the least common denominator.

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