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Unformatted text preview: ample: Solve for x: 6x – 2 = 8(x – 2) Solution: 6x – 2 = 8x – 16 14 = 2x x=7
r–s a–b www.petersons.com 120 Chapter 8 Exercise 2
Work out each problem. Circle the letter that appears before your answer. 1. Solve for x: 3x – 2 = 3 + 2x (A) 1 (B) 5 (C) –1 (D) 6 (E) –5 Solve for a: 8 – 4(a – 1) = 2 + 3(4 – a) (A) (B) (C) (D) (E) 3. (A) (B) (C) (D) (E)
5 3 7 – 3 4. Solve for x: .02(x – 2) = 1 (A) 2.5 (B) 52 (C) 1.5 (D) 51 (E) 6 Solve for x: 4(x – r) = 2x + 10r (A) 7r (B) 3r (C) r (D) 5.5r (E) 2r
1 3 2. 5. – 1 –2 2 48 14 6 1 2
1 1 y+6= y 8 4 Solve for y: www.petersons.com Concepts of Algebra—Signed Numbers and Equations 121 3. SIMULTANEOUS EQUATIONS IN TWO UNKNOWNS
In solving equations with two unknowns, it is necessary to work with two equations simultaneously. The object is to eliminate one of the unknowns, resulting in an equation with one unknown that can be solved by the methods of the previous section. This can be done by multiplying one or both equations by suitable constants in order to make the coefficients of one of the unknowns the same. Remember that multiplying all terms in an equation by the same constant does not change its value. The unknown can then be removed by adding or subtracting the two equations. When working with simultaneous equations, always be sure to have the terms containing the unknowns on one side of the equation and the remaining terms on the other side. Example: Solve for x: 7x + 5y = 15 5x – 9y = 17 Solution: Since we wish to solve for x, we would like to eliminate the y terms. This can be done by multiplying the top equation by 9 and the bottom equation by 5. In doing this, both y coefficients will have the same magnitude. Multiplying the first by 9, we have 63x + 45y = 135 Multiplying the second by 5, we have 25x – 45y = 85 Since the y terms now have opposite signs, we can eliminate y by adding the two equations. If they had the same signs, we would eliminate by subtracting the two equations. Adding, we...
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This note was uploaded on 08/15/2010 for the course MATH a4d4 taught by Professor Colon during the Spring '10 term at Embry-Riddle FL/AZ.
- Spring '10