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1 year ago

WRITING Explain how to solve the system of linear equations

Mathematics

1 answer:

Keith_Richards [23]1 year ago

3 0

Step-by-step explanation:

$2x - 3y = - 4.....(1) \\ - 5x + 9y = 7.....(2) \\ \\(1) \times 5 \\ 10x - 15y = - 20.....(3) \\ (2) \times 2 \\ - 10x + 18y = 14.....(4) \\ \\ (3) + (4) \\ 10x - 15y - 10x + 18y = - 20 + 14 \\ 3y = - 6 \\ y = - 2 \\ \\ (1) \\ 2x - 3 \times ( - 2) = - 4 \\ 2x + 6 = - 4 \\ 2x = - 10 \\ x = \frac{ - 10}{2} \\ x = - 5$

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9 months ago

Terry and Callie do word processing. For a certain prospectus Callie can prepare it two hours faster than Terry can. If they wor

Dahasolnce [82]

Time taken by jerry alone is 10.1 hours

Time taken by callie alone is 8.1 hours

Solution:

Given:- For a certain prospectus Callie can prepare it two hours faster than Terry can

Let the time taken by Terry be "a" hours

So, the time taken by Callie will be (a-2) hours

Hence, the efficiency of Callie and Terry per hour is $\frac{1}{a-2} \text { and } \frac{1}{a} \text { respectively }$

If they work together they can do the entire prospectus in five hours

$\text {So, } \frac{1}{a-2}+\frac{1}{a}=\frac{1}{5}$

On cross-multiplication we get,

$\frac{a+(a-2)}{(a-2) \times a}=\frac{1}{5}$

$\frac{2 a-2}{(a-2) \times a}=\frac{1}{5}$

On cross multiplication ,we get

$\begin{array}{l}{5 \times(2 a-2)=a \times(a-2)} \\\\ {10 a-10=a^{2}-2 a} \\\\ {a^{2}-2 a-10 a+10=0} \\\\ {a^{2}-12 a+10=0}\end{array}$

using quadratic formula:-

$x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

$x=\frac{12 \pm \sqrt{144-40}}{2}$

$\begin{array}{l}{x=\frac{12 \pm \sqrt{144-40}}{2}} \\\\ {x=\frac{12 \pm \sqrt{104}}{2}} \\\\ {x=\frac{12 \pm 2 \sqrt{26}}{2}} \\\\ {x=6 \pm \sqrt{26}=6 \pm 5.1} \\\\ {x=10.1 \text { or } x=0.9}\end{array}$

If we take a = 0.9, then while calculating time taken by callie = a - 2 we will end up in negative value

Let us take a = 10.1

So time taken by jerry alone = a = 10.1 hours

Time taken by callie alone = a - 2 = 10.1 - 2 = 8.1 hours

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2 years ago

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nataly862011 [7]

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