Question

By substitution method find x/2+2y/3=-1 and x-y/3=3

Answer 1

Thn putting the value of x in eq (1) u get value of x..

Answer 2

Given:

The linear equations in two variables:

$\frac{x}{2} +\frac{2y}{3} = -1 \ \ ......(1)\\\\ \& \ x - \frac{y}{3} = 3 \ \......(2)$ .

To Find:

The solution of the equations using substitution method.

Solution:

In substitution method, we first find the value of any one of the variables using anyone of the equations and then, substitute that value in another equation. Followed by, we solve the equation so obtained to get the solution.

Lets first find the value of x from equation (1):

$\frac{x}{2} +\frac{2y}{3} = -1\\ \\\Rightarrow \frac{x}{2} = -1 - \frac{2y}{3}\\ \\\Rightarrow \frac{x}{2} = \frac{-3-2y}{3}\\ \\\Rightarrow x = \frac{2}{3}(-3-2y)$

Now, we'll put the value of x in equation (2):

$x - \frac{y}{3} = 3\\ \\\Rightarrow \frac{2}{3}(-3-2y) - \frac{y}{3} = 3\\ \\\Rightarrow \frac{1}{3}[2(-3-2y)-y] = 3\\ \\\Rightarrow -6-4y-y = 3 \times 3\\ \\\Rightarrow -6 -5y = 9\\ \\\Rightarrow -5y = 9+6\\ \\\Rightarrow -5y = 15\\ \\\Rightarrow y = \frac{15}{-5}\\ \\\Rightarrow y =-3.$

Now, lets put the value of y in equation (2) {we always try to choose the equation which is easier to solve} :

$x - \frac{y}{3} = 3\\ \\\Rightarrow x - (\frac{-3}{3}) = 3\\ \\\Rightarrow x + 1 = 3\\\Rightarrow x = 3-1\\\Rightarrow x = 2.$

Therefore, we get the value of x & y as:

x = 2 and y = -3.