Question

solve for X and Y 2 upon X + 3 upon Y equal to 2 and 1 upon x minus 1 upon 2 y equals to 1 upon 3

Answer 1

Hey here is the answer....

Answer 2

Answer:

x=0,y=0  and x=2,y=3

Step-by-step explanation:

Given : Equations $\frac{2}{x}+\frac{3}{y}=2$....[1]

$\frac{1}{x}-\frac{1}{2y}=\frac{1}{3}$.....[2]

 In equation [1] take the LCM and solve

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

$\frac{2y+3x}{xy}=2$

$2y+3x=2xy$ .......[3]

 In equation [2] take the LCM and solve

$\frac{1}{x}-\frac{1}{2y}=\frac{1}{3}$

$\frac{2y-x}{2xy}=\frac{1}{3}$

$6y-3x=2xy$ .....[4]

Equation [3] and [4] has equal RHS therefore LHS are equal

$2y+3x=6y-3x$

$6x=4y$

$x=\frac{4}{6}y=\frac{2}{3}y$........[5]

Now, put the value of x in equation [3] and solve

$2y+3x=2xy$

$2y+3\times\frac{2}{3}y=2\times\frac{2}{3}y\times y$

$2y+2y=\frac{4}{3}\times y^2$

$4y\times3=4y^2$

$-4y^2+12y=0$

$-4y(y-3)=0$

Either y=0   or   y-3=0⇒y=3

Put the value of y in x i.e,[5],

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

If y=0

$x=\frac{2}{3}\times0=0$

If y=3

$x=\frac{2}{3}\times3=2$

Therefore, x any y are x=0,y=0 and x=2,y=3.

Points are (0,0) and (2,3).