Question

elimination method 2x+3y=2 and 3x+2y=4

Answer 1

Given equation :-

2x + 3y = 2 ....... ( i ) × 3

3x + 2y = 4 ..... ( ii ) × 2


Steps for elimination method :-

i ) Either the coefficient of x or the coefficient of y in both the equation should be equal.

ii ) For equal we have to multiply the equation by any positive integer.

In given equation we equal the coefficient of x by multiplying first equation by 3 and second by 2


Sub ( ii ) × 2 from ( i ) × 3


6x + 9y - ( 6x + 4y ) = 6 - 8

6x + 9y - 6x - 4y = - 2

5y = - 2

y = -2 /5


Putting the value of y in eq ( i )

2x + 3y = 2

2x + 3 × ( -2/5 ) = 2

2x - 6/5 = 2

( 10x - 6 )/5 = 2

10x - 6 = 10

10x = 10 + 6

10x = 16

x = 16/10

x = 1.6

Answer 2

First equation 2x+3y=2
second equation 3x+2y=4
for elimination method multiply first equation by 2 and second equation by 3.
$4x + 6y = 4 \: \: \: \: \: \: \: \: \: (1)\\ 9x + 6y = 12 \: \: \: \: \: \: \: (2) \\ by \: subtracting \: them \: we \: get \\ - 5x = - 8 \\ x = \frac{8}{5}$
now multiplying the first equation by 3 and second equation by 2.
$6x + 9y = 6 \\ 6x + 4y = 8 \\ by \: subtracting \: them \: we \: get \\ 5y = - 2 \\ y = \frac{ - 2}{5}$
value of x is 8/5
value of y is -2/5