Question

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By equation coefficients of variables solve the following equation.

$\\ x - 2y = - 10 \: ; \: 3x - 5y = - 12$
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Answer 1

Given:-

• $x - 2y = - 10 \: \: \: ...(1) \\ 3x - 5y = - 12 \: \: \: ...(2)$

To find:-

• The Value Of x and y

Solution:-

Finding The Value of y by 2nd Equation;

$3x - 5y = - 12 \: \: \: ...(2) \\ 3x - 5y = - 12 \\ - 5y = - 12 - 3x \\ \\ y = \frac{- 12 - 3x}{-5} \\ \\ y = \frac{ - 1(3x + 12)}{ - 1(5)} \\ \\ y = \frac{3x + 12}{5} \: \: \: ...(3)$

Substituting the Value of y in 1st Equation;

$x - 2y = - 10 \\ \\ x - 2( \frac{3x + 12}{5} ) = - 10 \\ \\ x - \frac{6x + 24}{5} = - 10 \\ \\ \frac{5x - 6x - 24}{5} = - 10 \\ \\ - x - 24 = - 10 \times 5 \\ - 1(x + 24) = - 50 \\ \\ x + 24 = \frac{ - 50}{ - 1} \\ x + 24 = 50 \\ x = 50 - 24 \\ \\ x = 26$

Finding The Value of y by Substituting the Value of x in 3rd Equation;

$y = \frac{3x + 12}{5} \: \: \: ...(3) \\ \\ y = \frac{3(26) + 12}{5} \\ \\ y = \frac{78 + 12}{5} \\ \\ y = \frac{90}{5 } \\ \\ y = 18$

Final Answer:-

• The Value Of x = 26
• The Value Of y = 18

Answer 2

Answer:

x = 26

y = 18

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Explanation:

We're given two equations:

• x - 2y = -10 ➝ Let this be Eq(1).

• 3x - 5y = -12 ➝ Let this be Eq(2).

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You can solve this any method you prefer, namely Elimination, Substitution and Cross-multiplication, I'll use the elimination method.

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In the elimination method, we add/subtract the given equations in a way that one of the variables (unknown values) gets eliminated from the resulting equation.

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So, let's multiply Eq(1) by 3, which gives us 3x - 6y = -30, and let this be Eq(3).

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If we subtract Eq(2) from Eq(3), we'll be able to eliminate the value of 'x' which will help us in finding the value of 'y'.

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[You can eliminate 'y' too, you just have to multiply both the equation by the required number to do so, it's your choice. Ultimately, we just need to eliminate one of the unknown values]

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So, on subtracting Eq(2) from Eq(3) we get;

➝ 3x - 6y - (3x - 5y) = -30 - (-12)

➝ 3x - 6y - 3x + 5y = -30 + 12

➝ - 6y + 5y = -30 + 12

➝ -y = -18

➝ y = 18

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Now we've got the value of 'y', and we need to find the value of 'x', for that we'll have to substitute the value of 'y' in one of the equations we've already got, let's substitute y's value in Eq(1).

[Once again, choosing an equation to substitute the value in is your choice]

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From Equation 1:

➝ x - 2y = -10

➝ x - 2(18) = -10

➝ x - 36 = -10

➝ x = -10 + 36

➝ x = 26

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Therefore, we've solved the given equation, with x = 26 and y = 18.