Answer to Question #15612 in Algebra for abid khan

Question

Linear Equations:
You know that x=(12)y+(12)(x+1) and y=(13)y+(13)(x+2) . What is x?What is y?

Answer 1

Here we have the initial system of two linear equations:

x = (12)y+(12)(x+1) (1)
y = (13)y+(13)(x+2) (2)

Let's rewrite it in a following form:

x = 12y + 12x + 12
y = 13y + 13x + 26

Now let's subtract the first equation from the second:

y - x = y + x + 14 ==> -2x = 14 ==> x = -7.

y = 13y + 13*(-7) + 26 ==> -12y = -65 ==> y = 65/12.

So, the solution is x=-7 and y=65/12.