The cost of each ream of paper is $4.5 and that of DVD is $5.
A system of linear equations is a group of equations having same number of variables and degree.
For the n number of variables n number of equations are required.
On the basis of number of solutions a system of equations can be classified as consistent and inconsistent.
Given that,
The price for 17 reams of paper and 12 DVDs is $136.50.
And, the price for 8 reams of paper and 21 DVDs is $141.
Suppose the cost of each ream of paper be x.
And, the cost of each DVD be y.
THen, the following equations can be made for the two cases,
17x + 12y = 136.50 (1)
8x + 21y = 141 (2)
Solve these equations by multiplying equation (1) by 7 and (2) by 4 and then subtracting them as,
7(17x + 12y) - 4(8x + 21y) = 7 × 136.50 - 4 × 141
=> 87x = 391.5
=> x = 4.5
Substitute x = 4.5 in equation (1) to get,
17 × 4.5 + 12y = 136.50
=> 12y = 136.50 - 76.50
=> 12y = 60
=> y = 5
Hence, the cost of each ream of paper and each DVD are $4.5 and $5 respectively.
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