Question

Solution of 3y/2-5x/3=-2 and y/3+x/3=13/16 by elimination method

Answer 1

Answer:

x = 159 / 304

y = 97 / 66

Given:-

$\frac{3y}{2} - \frac{5x}{3} = - 2 \: \: \: \: \: ...........(1)\\ \\ \frac{y}{3} + \frac{x}{3} = \frac{13}{16} \: \: \: \: \: \: \: \: \: .............(2)$

to find:-

• value of x and y

Solution:-

$\frac{3y}{2} - \frac{5x}{3} = - 2 \: \: \: \: \: \\ \\ \frac{10x - 9y}{6} = - 2 \\ \\ 10x - 9y = - 12 \: \: \: \: \: \: ..............(1) \\ \\ \frac{y}{3} + \frac{x}{3} = \frac{13}{16} \: \: \: \: \: \: \: \: \: \\ \\ \frac{3x + 3y}{9} = \frac{13}{16} \\ \\ \frac{3(x + y)}{9} = \frac{13}{16} \\ \\ \frac{16(x + y)}{3} = 13 \\ 16(x + y) = 13 \times 9 \\ \\ 16x + 16y = 39 \: ................(2) \\ \\ now \: muliply \: equation \: 1 \: by \: 16 \\ \\ 10x - 9y = - 12 \\ \\ 160x - 144y = - 192 \: ..............(3) \\ \\ multiply \: equation \: \: 2 \: \: by \: 9 \\ \\ 16x + 16y = 39 \\ \\ 144x + 144y = 351 \: ..........(4) \\ \\ now \: \: add \: the \: equation \: 3 \: \: and \: \: 4 \\ \\ \: \: \: 160x - 144y = - 192 \\ + 144x + 144y = 351 \\ - - - - - - - - - - - - \\ \: \: \: 304x \: \: = 159 \\ \\ \: \: \: \: \: \: \: \: x = \frac{159}{304} \\ \\ \: \: \: \: \: \: \: put \: \: x = \frac{159}{304} \: in \: equation \: 1 \\ \\ 10x - 9y = - 12 \\ \\ 10 \times \frac{159}{304} - 9y = - 12 \\ \\ \frac{1590}{304} - 9y = - 12 \\ \\ 1590 - 2736y = - 12 \times 304 \\ \\ - 2376y = - 3648 - 1590 \\ \\ - 2376y = - 5238 \\ \\ \: \: \: \: y = \frac{ - 5238}{ - 2376} \\ \\ y = \frac{2619}{1188} = \frac{873}{396} = \frac{291}{132} = \frac{97}{66}$

Answer 2

$x=\frac{543}{304},y=\frac{99}{152}$

Step-by-step explanation:

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

$\frac{9y-10x}{6}=-2$

$-10x+9y=-12$...(1)

$\frac{y}{3}+\frac{x}{3}=\frac{13}{16}$

$\frac{x+y}{3}=\frac{13}{16}$

$16x+16y=39$...(2)

Equation (1) multiply by 8 and equation (2) multiply by 5 and then adding equation (1) and (2)

$152y=99$

$y=\frac{99}{152}$

Substitute the values of y in equation(1)

$-10x+9(\frac{99}{152}=-12$

$10x=\frac{891}{152}+12=\frac{891+1824}{152}=\frac{2715}{152}$

$x=\frac{2715}{152\times 10}=\frac{543}{304}$

#Learn more:

https://brainly.in/question/5255641:Answered by Deepti