Question

Solve the following systems by Elmination by Substitution method.
6x+9y=11 ; 15x- 21y = 31
Answer x= 170/87 , y = -7/87

Answer 1

Hii friend,

6X +9Y = 11........(1)

15X -21Y = 31.......(2)

Using substitution method,

from equation 1 we get,

6X + 9Y = 11

6X = 11-9Y

X = 11-9Y/6......(3)

Putting the value of X in equation (2)

15X - 21Y = 31

15 × (11-9Y/6) -21Y = 31

11×15 - 15×9Y/6 -21Y = 31

165 - 135Y/6 - 21Y = 31

165-135Y - 126Y/6 = 31

165-135Y-126Y = 31 × 6

-261Y = 186-165

-261Y = 21

Y = 21/-261 = -7/87


Putting the value of Y in equation (3)

X = 11-9Y/6 = 11-9 × -7/87/6

X = 11+63/87/6 = 170/87

Hence,

X = 170/87 and Y = -7/87

Again, by elmination method

6X +9Y = 11.......(1)

15X - 21Y = 31.....(2)


Multiply equation (1) by 7 and equation (2) by 3 we get,


42X + 63Y = 77.......(3)

45X -63Y = 93......(4)


Subtract equation (3) by equation (4)

45X -63Y = 93
42X +63Y = 77
____________

87X = 170

X = 170/87


Putting the value of X in equation (1)

6X + 9Y = 11

6 × 170/87 + 9Y = 11

1020/87 + 9Y = 11

1020 + 783Y/87 = 11

1020 + 783Y = 11 × 87


1020 + 783Y = 957


783Y = 957-1020

Y = -63/783 = -7/87


Hence,

X = 170/87 and Y = -7/87



HOPE IT WILL HELP YOU....... :-)

Answer 2

6x + 9y = 11

9y = 11 - 6x

$y = \frac{11 - 6x}{9} \: \: \: \: \: \: - - - - - 1equation$



Now,


Putting the value of y in 15x - 21y = 31

--------------

$15x - 21( \frac{11 - 6x}{9} ) = 31 \\ \\ 15x - \frac{77 + 42x}{3} = 31 \\ \\ \frac{45x - 77 + 42x}{3} = 31 \\ \\ 87x - 77 = 93 \\ \\ 87x = 93 + 77 \\ \\ 87x = 170 \\ \\ x = \frac{170}{87} \: \: \: \: \: \: - - - - - 2equation$


From 2equation, we conclude that x = 170/87

Now,

Putting the value of x from 2equation to 1equation,


$y = \frac{11 - 6x}{9} \\ \\ y = \frac{11 - 6 \times \frac{170}{87} }{9} \\ \\ y = \frac{11 - \frac{1020}{87} }{9} \\ \\ y = \frac{ \frac{957 - 1020}{87} }{9} \\ \\ y = \frac{ - \frac{63}{87} }{9} \\ \\ y = - \frac{63}{87} \times \frac{1}{9} \\ \\ y = - \frac{7}{87}$




Then,

$x = \frac{170}{87}$

And

$y = - \frac{7}{87}$



I hope this will help you


-by ABHAY