Question

Solve the following pair of equation 43x + 67y = – 24 ; 67x + 43y = 24 by elimination method.
Plz ans step by step ​

Answer 1

Solution

Given =》

▪︎ 43x+67y= -24

▪︎ 67x+43y=24

Need to find =》

Value of x and y

Explanation =》

▪︎ 43x+67y= -24...........(1)

▪︎ 67x+43y=24..............(2)

On adding both equations

43x + 67y = -24

67x + 43y = 24

——————————

110x + 110y = 0

110(x+y)= 0

x+y=0................(3)

On subtracting both equations

43x + 67y = -24

67x + 43y = 24

- - -

——————————

-24x +24y = -48

24( -x+y)= -48

-x+y = -48/24

-x+y= -2................(4)

From equations 3 and 4

x + y = 0

-x + y = -2 on subtracting

+ - +

——————

2x = 2

x=1

putting x=1 in equation 3

x+y =0

1+y =0

y=-1

Answer 2

SOLUTION :

By Elimination Method :

• 43x + 67y = -24
• 67x + 43y = 24

Let suppose equation (1) & (2) :

$\longrightarrow\sf{43x+67y=-24.....................(1)}\\\\\longrightarrow\sf{67x+43y=24........................(2)}$

Multiply by 43 in equation (1) & multiply by 67 in equation (2),we get;

$\longrightarrow\sf{43(43x+67y=-24)}\\\\\longrightarrow\sf{1849x+2881y=-1032.....................(3)}$

&

$\longrightarrow\sf{67(67x+43y=24)}\\\\\longrightarrow\sf{4489x+2881y=1032.......................(4)}$

Subtracting equation (3) & equation (4),we get;

$\longrightarrow\sf{1849x-4489x\cancel{+2881y-2881y}=-1032-1032}\\\\\longrightarrow\sf{-2640x=-2064}\\\\\longrightarrow\sf{x=\cancel{-2064/-2640}}\\\\\longrightarrow\bf{x=43/55}$

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

$\longrightarrow\sf{43\bigg(\dfrac{43}{55} \bigg)+67y=-24}\\\\\\\longrightarrow\sf{\dfrac{1849}{55} +67y=-24}\\\\\\\longrightarrow\sf{1849+3685y=-1320}\\\\\\\longrightarrow\sf{3685y=-1320-1849}\\\\\\\longrightarrow\sf{3685y=-3169}\\\\\\\longrightarrow\sf{y=-3169/3685}$