Question

3x/2-5y/3=-2;x/3+y/2=13/6 in substitution method

Answer 1

i hope this will usful to u

Answer 2

Answer:

The value of x is 2 and y is 3.

Step-by-step explanation:

$\frac{3 x}{2}-\frac{5 y}{3}=-2$……………………..(1)

$\frac{x}{3}+\frac{y}{2}=\frac{13}{6}$……………………….(2)

Consider equation $\frac{3 x}{2}-\frac{5 y}{3}=-2$

 By taking LCM for the denominator 2 and 3 we get the LCM as 6

$\begin{array}{l}{\frac{3 x}{2} \times \frac{6}{6}=\frac{9 x}{6}} \\ {\frac{5 y}{3} \times \frac{6}{6}=\frac{10 y}{6}} \\ {\frac{9 x}{6}-\frac{10 y}{6}=-2}\end{array}$

9x – 10y = -12 ……………………….. (3)

Consider equation 2

$\frac{x}{3}+\frac{y}{2}=\frac{13}{6}$

By taking LCM for the denominator 3 and 2 we get the LCM as 6

$\begin{array}{l}{\frac{x}{3} \times \frac{6}{6}=\frac{2 x}{6}} \\ {\frac{y}{2} \times \frac{6}{6}=\frac{3 y}{6}} \\ {\frac{2 x}{6}+\frac{3 y}{6}=\frac{13}{6}}\end{array}$

2x + 3y = 13 …………………………(4)

By solving equation (3) and (4) we get

2x = 13-3y

x=13-3y/2 …………………………(5)

Put the value of x in eqn 3 we get

9[13-3y/2] – 10y =-12

117-27y-20y = -24                  [By taking LCM and solving it]

117-47y=-24

-47y=-24-117

-47y=-141

Y=-141/-47

Y=3

Now put the value of y =3 in (5)

x=13-3(3)/2

x=13-9/2

x=4/2

x=2

Therefore we have x=2 and y=3