Question

3x+4y=30,x+2y=12 by substitution method

Answer 1

Answer:

x=6; y=3

Given:

3x+4y = 30.........equation (1)

x+ 2y = 12.............equation (2)

In elimination method, we need to manipulate the equations in such manner that one of the variables gets eliminated  and only one variable remains.

So multiplying equation (2) by 3 we get

3x + 6y = 36

Now subtracting the above equation from equation (1) we get-

3x + 4y - 3x - 6y = 30 - 36

or -2y = -6

or y = 3

Putting the value of y in equation (1) , we get

3x + 4*3 = 30

or 3x = 30-12= 18

or x= 6

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Answer 2

Answer:

$3x + 4y = 30 \: - - - (i)$

$x + 2y = 12 \: - - - - (ii)$

$from \: (ii) \: x = 12 - 2y - - - - (iii)$

$substitute \:eq \: (iii) \: in \: eq \: (i)$

$3(12 - 2y) + 4y = 30$

$36 - 6y + 4y = 30$

$36 - 2y = 30$

$- 2y = 30 - 36$

$- 2y = - 6$

$y = \frac{ - 6}{ - 2}$

$y = 3$

substitute value of y in (iii)

x = 12-2y

= 12-2(3)

= 12-6

= 6