1. Key answers

2. A. SOLVING LINEAR EQUATIONS BY SUBSTITUTION & ELIMINATION METHOD 8. In the system of this type, multiply so that the numerators are equal and the variable with equal numerators can be eliminated. SOLUTION: Multiply the 1 st equation by 4. Then add the result to the 2 nd equation.

3. A. SOLVING LINEAR EQUATIONS BY SUBSTITUTION & ELIMINATION METHOD SOLUTION: Multiply the 1 st equation by 4. Then add the result to the 2 nd equation. +

4. A. SOLVING LINEAR EQUATIONS BY SUBSTITUTION & ELIMINATION METHOD SOLUTION: To find x, substitute the value of y in any equation. The solution is (3/2, 5/3)

5. B. CONSSITENT,INCONSISTENT, DEPENDENT 1. 7: 14 = (-2) : (-4) ≠ 7:6 (inconsistent) 6. 2:6 = 1:3 = 5:15 (dependent) The rest are consistent

6. C. CONSSITENT,INCONSISTENT, DEPENDENT 1. Any value of y will make the system consistent as 1: 3 ≠ (-2) : 1 2. 2:4 = (-1):(-2) =7:k If k =14, the system will be dependent; if k ≠ 14, the system is inconsistent.

7. C. CONSSITENT,INCONSISTENT, DEPENDENT 3. 3:1 = 9:3 =6:k If k =2, the system will be dependent; if k ≠ 2, the system is inconsistent.

8. D. PROBLEM SOLVING 1. X = 30, the smaller number X + 15 = 45, the bigger number 2. let x be the smaller number 900-x, the larger 0.04(900-x) + 0.07x = 48 x = 400 (smaller number) & 900-x = 500, (bigger number)

9. D. PROBLEM SOLVING 3. X = P60, the cost of the belts y = P130, the cost of the hats 4. let x be the tens digit 11-x, the ones digit x = 3 11- x = 8, therefore the number is 38.

10. D. PROBLEM SOLVING 5. X = age of the son 4x = age of Mr. Carlos So, x = 10 years, 4x = 40 years 6. let x be the money of A y pesos, the money of B x = 10 & y = 30

11. Challenge 1. let x meter (m) be the width of the pool The length be 1.5 x. The outer width is (x + 2)m The outer length is (1.5x + 2)m The area of a path = (1.5x + 2)(x+2)- x(1.5 x) = 44 5x + 4 = 44 5x = 40 x = 8 m, the width of the pool 1.5 x = 12 m, the length of the pool

12. 2. let x be the number of the guest ½ x,the number of bowls of rice 1/3 x,the number of bowls of broth ¼ x,the number of bowls of meat 6x + 4x + 3x = 12(65) 13x = 12 (65) x = 60, the number of guest

13. 3. let x be pesos the cost of bracelet y, the cost of watchband z,the cost of a locket x + y = 500 (eq. 1) y + z = 600 (eq. 2) z + x = 700 (eq. 3) 2x +2y +2z = 1800 x +y +z = 900 rewrite eq. 1, y = 500 - x x +y +z = 900 x + 500-x +z =900 z= 900-500 z = P400 y = P200 x = P300