Question

solve the equation
x+2y=8and 2x-2y=4
​

Answer 1

Answer:

x=4 and y=2

Step-by-step explanation:

First we will make one of the equations in terms of x or y

x+2y=8   ⇒2y=8-x   ⇒y=(8-x)/2

Now substituting y in the other equation,

2x-2(8-x)/2=4   ⇒3x-8=4   ⇒3x=12 ⇒x=4

Now substituting x in the y,

y=(8-4)/2  ⇒y=2

Answer 2

x + 2y = 8 => Equation 1

2x - 2y = 4 => Equation 2

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x + 2y = 8

x = 8 - 2y

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Substituting the value of x as 8 - 2y in Equation 2,

2x - 2y = 4

2(8 - 2y) - 2y = 4

16 - 4y - 2y = 4

16 - 6y = 4

Transposing the constants to one side and the variables to the other,

16 - 4 = 6y

12 = 6y

Transposing 6 to the LHS,

$\dfrac{12}{6} = y$

By reducing to the lowest terms,

2 = y

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Hence,

x = 8 - 2y

x = 8 - 2(2)

x = 8 - 4

x = 4

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Verification :-

Substituting x and y as 4 and 2 respectively,

EQUATION 1 :-

x + 2y = 8

4 + 2(2) = 8

4 + 4 = 8

LHS = RHS

EQUATION 2 :-

2x - 2y = 4

2(4) - 2(2) = 4

8 - 4 = 4

LHS = RHS

Therefore verified.

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