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1 year ago

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7x + 8y = 25 9x + 10y =35 elimination method please

1 answer:

djverab [1.8K]1 year ago

3 0

$7x +8y = 25 ~~~....(i)\\\\9x +10y = 35~~~ ....(ii)\\\\\text{Multiply equation (ii) by}~ \dfrac 79 ~ \text{and do (ii) - (i):}\\\\\dfrac 79 (9x +10y) - (7x +8y) = \dfrac 79 (35) - 25\\\\\\\implies 7x +\dfrac{70y}9 - 7x -8y = \dfrac{245}9 -25\\\\\\\implies - \dfrac{2y}9 = \dfrac{20}9\\\\\\\implies -2y =20\\\\\implies y =-10\\\\\text{Substitute}~ y = -10~ \text{in equation (i):}\\\\\\7x +8(-10) = 25\\\\\implies 7x = 25 +80\\\\\implies 7x = 105 \\\\\implies x =15\\\\$

$\\\text{Hence}~ (x,y) = (15,-10)$

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Step-by-step explanation:

Given

a_1 = 5

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First of all we have to calculate the common ratio of the sequence. The common ratio is the ratio between two consecutive terms of a geometric sequence.

So,

$r=\frac{a_2}{a_1} = \frac{15}{5} = 3$

The explicit formula for geometric sequence is:

$a_n = a_1.r^{n-1}$

Putting the value of r and a_1

$a_n = 5.(3)^{n-1}$

Putting n=3 in the explicit formula

$a_3 =5.3^{3-1}\\= 5 * 3^2\\=5 * 9\\= 45$

Putting n=10 for tenth term

$a_{10} =5.3^{10-1}\\=5*3^9\\=5 * 19683\\=98415$

Hence,

a_3 is 45 and a_10 is 98415

Keywords: Geometric sequence, Explicit formula

Learn more about geometric sequence at:

#LearnwithBrainly

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Step-by-step explanation:

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