Write the system of linear equation and solve the solution using Elimination method.?

 Lucy’s sports store can order basketballs and footballs in two different ways. 

 A box of 4 basketballs and 3 footballs costs ₱1 005.00. 

 A bag of 3 basketballs and 5 footballs costs ₱1 115.00. 

 how much does each ball cost?

 4b + 3f = 1005

 3b + 5f = 1115

 b ≈ 152.73, f ≈ 131.36

Let b - basketballs

 f - footballs

 5[4b + 3f = 1005.00]

 3[3b + 5f = 1115.00]

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20b + 15f =5025

-[9b + 15f = 3345]

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11b =1680

 b = 152.72 pesos    Answer//

solving for f

4b + 3f = 1005

3f = 1005 - 4b

........1005 - 4b

f = -------------------

.............3

........1005 - 4(152.72)

f =  --------------------------

..................3

f = 131.37 pesos  answer//

Simultaneous Equations 

4B + 3F = 1005

3B + 5F = 1115

Multiply the top eq'n by '3' and the bottom eq'n by '-4' . then add the two equations. This will eliminate 'B'. 

Hence 

12B + 9F = 3015

-12B - 20F = -4460

-11F = - 1445

Divide through by '-1' 

11F = 1445 

Divide both sides by '11' 

F = 1445/11 = 131.36 is the cost of one football 

substitute this value into one of the original equations for 'B' 

4B + 3(131.36) = 1005

4B + 394.09 = 1005

4B = 610.91

B = 610.91/4 = 152.72 is the cost of one basketball. 

4B + 3F = 1005.00;

3B + 5F = 1115.00.

Multiply the 2nd equation by 0.6, you get

1.8B + 3F = 669.00.

Subtract that from the very first equation, you get

2.2B = 336.00, which implies

B = 152.73 and 

F = (1005.00 - 4B)/3

= 131.96.