Key answers

A. SOLVING LINEAR EQUATIONS BY SUBSTITUTION & ELIMINATION

METHOD8. 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 1st equation by 4. Then add the

result to the 2nd equation.

202012

553

4553

yxyxyx

A. SOLVING LINEAR EQUATIONS BY SUBSTITUTION & ELIMINATION

METHODSOLUTION:Multiply the 1st equation by 4. Then add the

result to the 2nd equation.

3

521

35

2135

y

y

y

+

3

521

35

2135

y

y

y

A. SOLVING LINEAR EQUATIONS BY SUBSTITUTION & ELIMINATION

METHODSOLUTION:To find x, substitute the value of y in any

equation.

2

3

23

533

55

35

3

x

x

xx

The solution is (3/2, 5/3)

B. CONSSITENT,INCONSISTENT, DEPENDENT1. 7: 14 = (-2) : (-4) ≠ 7:6 (inconsistent)

6. 2:6 = 1:3 = 5:15 (dependent)

The rest are consistent

C. CONSSITENT,INCONSISTENT, DEPENDENT1. Any value of y will make the system consistent as 1: 3 ≠ (-2) : 1

2. 2:4 = (-1):(-2) =7:kIf k =14, the system will be dependent; if k ≠ 14, the system is inconsistent.

C. CONSSITENT,INCONSISTENT, DEPENDENT

3. 3:1 = 9:3 =6:kIf k =2, the system will be dependent; if k ≠ 2, the system is inconsistent.

D. PROBLEM SOLVING1. X = 30, the smaller numberX + 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)

D. PROBLEM SOLVING3. 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.

D. PROBLEM SOLVING5. X = age of the son 4x= age of Mr. CarlosSo, x = 10 years, 4x = 40 years

6. let x be the money of A y pesos, the money of B x = 10 & y = 30

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

Challenge 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

65432

xxx

Challenge 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= 900-500z = P400 y = P200 x = P300