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Additional info for Algebra II (Cliffs Quick Review)
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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