/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 96 Evaluate \(x^{2}-(x y-y)\) for \... [FREE SOLUTION] | 91影视

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Chapter 6: Problem 96

Evaluate \(x^{2}-(x y-y)\) for \(x\) satisfying \(\frac{3 x}{2}+\frac{3 x}{4}=\frac{x}{4}-4\) and \(y\) satisfying \(5-y=7(y+4)+1\).

Short Answer

Expert verified
The value for \(x^{2} - (xy - y)\) when \(x = -\frac{16}{11}\) and \(y = \frac{23}{4}\) is approximately 105.12.

Step by step solution

01

Expressing \(x\) and \(y\) from the equations

Firstly, by rearranging the first equation \(\frac{3x}{2} + \frac{3x}{4} = \frac{x}{4} - 4\) a single value for \(x\) can be found. Combine like terms to get \(\frac{11x}{4} = -4\). Multiply both sides by \(\frac{4}{11}\) to yield \(x = -\frac{16}{11}\). For the second equation, \(5 - y = 7(y+4) + 1\), isolate \(y\) to get \(y = \frac{46}{8} = \frac{23}{4}\).
02

Substitution into the original equation

Substitute the found values of \(x\) and \(y\) into the equation \(x^{2} - (xy - y)\). This yields \(\left(-\frac{16}{11}\right)^{2} - \left(-\frac{16}{11}\cdot\frac{23}{4} - \frac{23}{4}\right) = \frac{256}{121} - \left(-\frac{736}{44} - \frac{92}{4}\right) = \frac{256}{121} - \left(-\frac{1168}{44}\right) = \frac{256}{121} + \frac{1168}{11}\). Calculating this gives a value of approximately 105.12.

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