Given r=(3-x/y) p=(2x/x +y/-3) and q= (7+x/10) . If r + p = q find the value of x and y?

To find the values of x and y, we first need to simplify the expressions for r, p, and q:

r = (3 - x/y)
p = (2x/x + y/-3)
q = (7 + x/10)

Now, let's substitute these expressions into the equation r + p = q:

(3 - x/y) + (2x/x + y/-3) = (7 + x/10)

Simplify the expression:

3 - x/y + 2 + y/-3 = 7 + x/10
5 - x/y + y/-3 = 7 + x/10
5 - x/y - y/3 = 7 + x/10

Now, we need to find common denominators to combine the terms:

(15 - 3x - y)/3y = (70 + 3x)/10

Now, cross multiply to solve for x and y:

10(15 - 3x - y) = 3y(70 + 3x)
150 - 30x - 10y = 210y + 9x

Combine like terms:

9x - 30x = 210y + 10y - 150
-21x = 220y - 150

Now, we can solve for x in terms of y:

x = (220y - 150)/-21

To find the value of y, we need to substitute this expression for x back into one of the original equations. Let's use the equation r = (3 - x/y):

r = (3 - (220y - 150)/(-21)y)

Now, we can solve for y:

r = (3 + (220y - 150)/21y)
r = (3(21y) + 220y - 150)/21y
r = (63y + 220y - 150)/21y
r = (283y - 150)/21y

Since r = q, we can set these two expressions equal to each other:

(283y - 150)/21y = (7 + x/10)

Now, substitute the expression for x back in terms of y:

(283y - 150)/21y = (7 + (220y - 150)/(-21)10)

Solve for y:

(283y - 150)/21y = (7 + (220y - 150)/(-210))

This equation can be solved to find the values of x and y.