Thread: algebra, values pf x and y

two questions:
x over x - 9 = 4 over 7
x + y over x - y = 5 over 3 .
that is one question, find x and y, show all steps please...
the 2nd one.
x - 3 over 4 = y +2 over 2
x +y-1 over 6 = x - y + 1 over 5.
show all steps thanks

Originally Posted by gamecube10074

two questions:
x over x - 9 = 4 over 7
x + y over x - y = 5 over 3 .
that is one question, find x and y, show all steps please...

x/(x - 9) = 4/7
(x + y)/(x - y) = 5/3

I'm assuming you're trying to solve this system of equations.

x = 4/7*(x-9)

7x = 4*(x - 9)

7x = 4x - 36

36 = -3x

x = -12 -- (1)

(x + y)/(x - y) = 5/3

x + y = 5/3*(x - y)

x + y = 5/3x - 5/3y

y = (2x)/3 - (5y)/3

3y = 2x - 5y

8y = 2x

y = x/4

But, from (1), we can substitute x in for y;

y = (-12)/4

y = -3

Thus, we have (-12, -3)

Originally Posted by gamecube10074

the 2nd one.
x - 3 over 4 = y +2 over 2
x +y-1 over 6 = x - y + 1 over 5.
show all steps thanks

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

Multiply both sides by 4;

x - 3 = 2*(y + 2)

x - 3 = 2y + 4

x = 2y + 7 -- (1)

(x + y - 1)/6 = (x - y + 1)/5

Multiply both sides by 30;

5*(x + y - 1) = 6*(x - y +1)

5x + 5y - 5 = 6x - 6y + 6

5y = x - 6y + 11

11y = x + 11

y = (x + 11)/11

Substitute:

y = ([2y + 7] + 11)/11

11y = 2y + 7 + 11

11y = 2y + 18

9y = 18

y = 2

And thus,

x = 2(2) + 7

x = 11

The final answer: (11, 2)