Download Cliffs QuickReview algebra 1 by Jerry Bobrow PDF

By Jerry Bobrow

ISBN-10: 076456370X

ISBN-13: 9780764563706

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X - 3 = 13 x Example 5: Express the answers with positive exponents. (a) a - 2 b = b2 a -3 (b) a 4 = 31 b a b4 (c) ` a 2 b - 3 j ` a - 1 b 4 j = ab R 2 -1 V Sa $ a = a W S -3 4 W Sb $ b = b W T X Polynomials A polynomial consists of two or more terms. For example, x + y, y2 – x2, and x2 + 3x + 5y2 are all polynomials. A binomial is a polynomial that consists of exactly two terms. For example, x + y is a binomial. A trinomial is a polynomial that consists of exactly three terms. For example, y2 + 9y + 8 is a trinomial.

Example 5: Solve for x and y. x=y+8 x + 3y = 48 From the first equation, substitute (y + 8) for x in the second equation. (y + 8) + 3y = 48 Now solve for y. Simplify by combining y’s. 4y + 8 = 48 -8 -8 4y = 40 4y 40 = 4 4 y = 10 Now insert y = 10 in one of the original equations. x=y+8 x = 10 + 8 x = 18 Answer: y = 10, x = 18 Chapter 5: Equations with Two Variables 53 Graphing method Another method of solving equations is by graphing each equation on a coordinate graph. The coordinates of the intersection will be the solution to the system.

Example 3: Solve for a and b. 3a + 4b = 2 6a + 8b = 4 The second equation is actually the first equation multiplied by 2. In this instance, the system is unsolvable. Example 4: Solve for p and q. 3p + 4q = 9 2p + 2q = 6 Multiply the second equation by 2. (2)2p + (2)2q = (2)6 4p + 4q = 12 Now subtract the equations. 3p + 4q = 9 ^ - h 4p + 4q = 12 -p = -3 p = 3 52 CliffsQuickReview Algebra I Now that you know p = 3, you may plug in 3 for p in either of the two original equations to find q. 3p + 4q = 9 3(3) + 4q = 9 9 + 4q = 9 4q = 0 q=0 Answer: p = 3, q = 0 Substitution method Sometimes a system is more easily solved by the substitution method.

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