Question

2x+5y=8/3, 3x-2y=5/6​

Answer 1

Given: 2x + 5y = 8/3, 3x - 2y = 5/6​.

To find: The value of x and y.

Answer:

Let us solve this using the substitution method.

Take this - 2x +  5y = 8/3 - as equation 1; 3x - 2y = 5/6​ - as 2.

From 1,

2x + 5y = 8/3

5y = 8/3 - 2x

5y = 8/3 - 6x/3

$\sf y =$  $\sf \frac{8\ -\ 6x}{15}$  

Now, substituting the value of y (solved above) in equation 2.

$\sf 3x\ -\ 2(\frac{8\ -\ 6x}{15})\ =\ \frac{5}{6}\\\\3x\ -\ (\frac{16\ -\ 12x}{15})\ =\ \frac{5}{6}\\\\\frac{45x\ -\ 16\ +\ 12x}{15}\ =\ \frac{5}{6}\\\\\frac{57x\ -\ 16}{15}\ =\ \frac{5}{6}\\\\57x\ -\ 16 = \frac{75}{6}\\\\57x\ =\ \frac{75}{6}\ +\ 16\\ \\57x\ =\ \frac{75\ +\ 96}{6}\\ \\57x\ =\ \frac{171}{6}\\ \\x\ =\ \frac{171}{342}\\\\x = \frac{1}{2}$

We now have the value of x. Let us use this to find the value of y.

(Using equation 1),

2x + 5y = 8/3

2(1/2) + 5y = 8/3

1 + 5y = 8/3

5y = 8/3 - 1

5y = 8/3 - 3/3

5y = 5/3

y = 1/3

Therefore, x = 1/2 and y = 1/3.

Answer 2

Answer:

2x + 5y = 8/3

6x + 15y =8....(1)×3

3x - 2y =5/6

18x - 12y =5....(2)

18x + 45y = 24

18x - 12y = 5

-. +. -

57y =. 19

y = 19/57

y = 1/3

put y = 1/3 in eqn ...(1)

6x + 15y = 8

6x + 15×1/3 = 8

6x + 5 = 8

6x = 8- 5

6x = 3

x = 3/6

x = 1/2

solutions of (x,y) = (1/2, 1/3)