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2 years ago

2x − y = 3

Mathematics

1 answer:

const2013 [10]2 years ago

5 0

Answer:

a. Infinitely many solutions

Step-by-step explanation:

The given equations are 2x - y = 3

4x = 6 + 2y

We can use substitution method to solve these system of equations.

2x - y = 3

y = 2x - 3

Now plug in y = 2x - 3 in the second equation, we get

4x = 6 + 2(2x - 3)

4x = 6 + 4x - 6

4x = 4x

Here we get infinitely many solution.

Both the equations are the same.

Thank you.

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The sum of an infinite geometric series is three times the first term. Find the common ratio of this series.

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Answer:

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Step-by-step explanation:

The sum of an infinite geometric series is expressed according to the formula;

$S_\infty = \dfrac{a}{1-r}$ where;

a is the first term of the series

r is the common ratio

If the sum of an infinite geometric series is three times the first term, this is expressed as $S_\infty = 3a$

Substitute $S_\infty = 3a$ into the formula above to get the common ratio r;

$3a = \dfrac{a}{1-r} \\\\$

$cross \ multiply\\\\3a(1-r) = a\\\\3(1-r) = 1\\$

open the parenthesis

$3 - 3r = 1\\\\$

subtract 3 from both sides

$3 - 3r -3= 1-3\\\\-3r = -2\\\\r = \frac{2}{3}$

<em>Hence the common ratio of this series is </em> $\frac{2}{3}$ <em></em>

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Answer:

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Step-by-step explanation:

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1 year ago

Read 2 more answers