Question

41x - 17y= 99; 17x - 41y = 75 by elimination method

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Answer 1

Answer:

Adding and subtracting the 2 equations.

Subtracting:

41x - 17y = 99

17x - 41y = 75

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24x + 14y = 24

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Therefore x + y =1

Adding:

41x - 17y = 99

17x - 41y = 75

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58x - 58y = 174

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Therefore x - y = 3

Now simplifying the 2 equations x + y =1 and x - y = 3 we get

Y = -1; x = 2

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Answer 2

Answer: The value of x and y is 2 and -1.

Explanation-

Given-The two-equation is $41x-17y=99, 17x-41y=75$

Find the value of x and y by the elimination method.

Solution-The elimination method is the process of eliminating one of the variables in the system of linear equations using the addition or subtraction methods in conjunction with multiplication or division of coefficients of the variables.

The substitution method is the algebraic method to solve simultaneous linear equations. As the word says, in this method, the value of one variable from one equation is substituted in the other equation.

So, the given equation is-

$41x-17y=99$......(1)

$17x-41y=75....2$

First, we subtracting these two equations 1 and 2.

$41x-17y=99$.....(1)

$17x-41y=75$

$24x+24y=24$

$x+y=1$....(3)

Now add these two equations (1) and (2)

$41x-17y=99$....(1)

$17x-41y=75$......(2)

$58x-58y=174$

$x-y=3$.....(4)

Now square equation (3) and (4)

$x+y=1$

$x-y=3$

$2x=4$

$x=2$

This value of x putting equation (3)

$2+y=1$

$y=-1$

So, the value of x and y is 2 and -1.

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