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Chapter 11: Problem 6

If \(6 k-5 l=27\) and \(3 l-2 k=-13\) and \(5 k-5 l=j,\) what is the value of \(j ?\)

Short Answer

Expert verified
The value of j is 25.

Step by step solution

01

Solve the first two equations

To solve the first two equations, one needs to rearrange and eliminate either k or l. Multiplying the first equation by 2 and the second by 3:\(12k - 10l = 54\) and \(9l - 6k = -39\). Adding these two equations gives: \(12k - 10l + 9l - 6k = 54 - 39\), which simplifies to \(6k - l = 15\). After finding l in terms of k, the value of k is found.
02

Find the value of l using the first equation

Substitute \(6k - 15\) for \(l\) in the first equation: \(6k - 5(6k - 15) = 27\), this simplifies to \(6k - 30k + 75 = 27\), further simplifying gives \(-24k = -48\) therefore, \(k = 2\). Substituting \(k = 2\) into \(6k - l = 15\) gives \(l = -3\).
03

Substitute k and l into the third equation

Substitute \(k = 2\) and \(l = -3\) into the third equation: \(5k - 5l = j\), which simplifies to \(5*2 - 5*(-3) = j\), therefore, \(j = 25\).

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