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Tcecarenko [31]
2 years ago
8

Solve the system: 2/x - 3/y =-5; 4/x + 6\y =14

Mathematics
1 answer:
sertanlavr [38]2 years ago
3 0

The solution is x = 2 \text{ and } y = \frac{1}{2}

<em><u>Solution:</u></em>

Let us assume,

a = \frac{1}{x}\\\\b = \frac{1}{y}

<em><u>Given system of equations are:</u></em>

\frac{2}{x} - \frac{3}{y} = -5

\frac{4}{x} + \frac{6}{y} = 14

<em><u>Rewrite the equation using "a" and "b"</u></em>

2a - 3b = -5 ------------ eqn 1

4a + 6b = 14 -------------- eqn 2

<em><u>Let us solve eqn 1 and eqn 2</u></em>

<em><u>Multiply eqn 1 by 2</u></em>

2(2a - 3b = -5)

4a - 6b = -10 ------------- eqn 3

<em><u>Add eqn 2 and eqn 3</u></em>

4a + 6b = 14

4a - 6b = -10

( - ) --------------------

8a = 4

a = \frac{4}{8}\\\\a = \frac{1}{2}

Substitute a = 1/2 in eqn 1

2(\frac{1}{2}) -3b = -5\\\\1 - 3b = -5\\\\3b = 6\\\\b = 2

Now let us go back to our assumed values

Substitute a = 1/2 in assumed values

a = \frac{1}{x}\\\\\frac{1}{2} = \frac{1}{x}\\\\x = 2

Substitute b = 2 in assumed value

b = \frac{1}{y}\\\\2 = \frac{1}{y}\\\\y = \frac{1}{2}

Thus the solution is x = 2 \text{ and } y = \frac{1}{2}

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3 years ago
2(1 − x) = 9(1 + 2x) + 52(1 − x) = 9(1 + 2x) + 5
marusya05 [52]

Solving the equation 2(1-x) = 9(1 + 2x) + 5 we get x=-\frac{3}{5}

Step-by-step explanation:

We need to solve the equation 2(1-x) = 9(1 + 2x) + 5 and find value of x

Solving:

2(1-x) = 9(1 + 2x) + 5\\2-2x=9+18x+5\\Adding\,\,-18x\,\,on\,\,both\,\,sides:\\2-2x-18x=9+5\\Adding\,\,-2\,\,on\,\,both\,\,sides\\-20x=14-2\\-20x=12\\x=\frac{12}{-20}\\x=-\frac{3}{5}

So, solving the equation 2(1-x) = 9(1 + 2x) + 5 we get x=-\frac{3}{5}

Keywords: Solving Equations

Learn more about Solving Equations at:

  • brainly.com/question/1563227
  • brainly.com/question/2403985
  • brainly.com/question/11229113

#learnwithBrainly

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The perimeter of a rectangular garden is 52 feet the length of the garden is 4 less than twice the width what is the widththe
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