Question

Solve this,
Solve by substitution.
X-y/2=3 , x/2 - 2y/3 = 2/3

Answer 1

Given: The two equations x - y/2 = 3 , x/2 - 2y/3 = 2/3

To find: Solve for x and y using substitution.

Solution:

• Now we have two equations:

                 x - y/2 = 3  ...................(i)

                 x/2 - 2y/3 = 2/3     ...................(ii)

• Now from (i), we have:

                 x = 3 + y/2

                 x = (6 + y )/ 2

• Putting this value of x in (ii), we get:

                 (6 + y )/ 2/2 - 2y/3 = 2/3

                 (6 + y )/ 4 - 2y/3 = 2/3

• Now simplifying, we get:

                 ( 3(6 + y ) - 4(2y) ) / 12 = 2/3

                 ( 18 + 3y - 8y ) / 12 = 2 / 3

                 18 - 5y = 24 / 3

                 18 - 5y = 8

                 10 = 5y

                 y = 2

• Putting y = 2 in (i), we get:

                 x - 2/2 = 3

                 x - 1 = 3

                 x = 4

Answer:

           So the value of x is 4 and y is 2.

Answer 2

GIVEN :

The equations are $\frac{x-y}{2}=3$ and $\frac{x}{2}-\frac{2y}{3}=\frac{2}{3}$

TO FIND :

The values of a and y in the given equations by using Substitution Method.

SOLUTION :

Given that the equations are

$\frac{x-y}{2}=3\hfill (1)$ and

$\frac{x}{2}-\frac{2y}{3}=\frac{2}{3}\hfill (2)$

Now solving the given equations by using Substitution Method.

From the equation (1) we have

$\frac{x-y}{2}=3$

$x-y=3\times 2$

$x-y=6$

∴ $x=y+6\hfill (3)$

Equation (2) becomes,

$\frac{x}{2}-\frac{2y}{3}=\frac{2}{3}$

$\frac{3x-4y}{6}=\frac{2}{3}$

$3x-4y=\frac{2}{3}\times 6$

$3x-4y=4\hfill (4)$

Now substituting the value x=y+6 in the equation (4) we get,

3(y+6)-4y=4

3(y)+3(6)-4y=4

By using the Distributive property :

a(x+y)=ax+ay

3y+18-4y=4

-y=4-18

-y=-14

∴ y=14

By substituting the value of y in the equation (3) we have that,

x=14+6

∴ x=20

∴ the values of x and y in the given equations is 20 and 14 respectively.

∴ the solution is (20,14).