Question

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

Answer 1

2x + 3y = 2..........1)
3x + 2y = 4..........2)
Multiplying 1) by 3 we get, 6x + 9y = 6
Multiplying 2) by 2 we get, 6x + 4y = 8
(-) (-) (-)
Subtracting 2) from 1) we get, 0 + 5y = -2
y = -2/5
Putting the value of y in 2) we get,
3x + 2*(-2/5) = 4
or, 3x - 4/5 = 4
or, 3x = 24/5
or, x = 8/5

Answer 2

2x + 3y = 2 ... (A)
3x + 2y = 4 ... (B)

Multiply equation (A) with 3 and equation (B) with 2.
→( 2x + 3y = 2 ) × 3
    6x + 9y = 6 ... (i)
→( 3x + 2y = 4 ) × 2
     6x + 4y = 8 ...(ii)

+6x   +   9y   =  +6
+6x   +   4y   =  +8
-        -               -
_______________
              5y   =  -2
                y   =  -2/5
put the value of y in equation (A), 
2x + 3y = 2
2x + 3(-2/5) = 2
2x + (-6/5)= 2
2x - 6/5 = 2
→take the LCM of 1 and 5.
10x/5 - 6/5 = 2
( 10x - 6 )/5 = 2
10x - 6 = 5 × 2
10x - 6 = 10
10x = 10 + 6
10x = 16
x = 16/10
x = 1.6
 by putting the value of y in equation (A), we get
x = 1.6 and y = -2/5.