Question 1043539

Ref. Question 1043454:

Please list the operations you did after you substituted for y.  I still don't understand.  Sorry.
<pre>You seem to want to use 2 equations to solve for x, in terms of 3 other variables. Why didn't you say so when question 1043447 was submitted? 

Question 1043447: If a is added to the difference of 2 quantities, the sum is b, and if the larger is divided by the smaller, the quotient is c. Determine quantities. 
Let x = larger
Let y = smaller 
My attempt: 
x - y + a = b 
x / y = c 
How do I proceed ? 

Apparently, you want to solve for x using the following equations: 
x - y + a = b______y = x + a - b ------ eq (i)
{{{matrix(1,8, x/y = c,"=====>", cy = x, "========>", y = x/c, "------", eq, (ii))}}}
Since y = x + a - b, and {{{y = x/c}}}, it follows that: {{{x + a - b = x/c}}}
cx + ac - bc = x ------- Multiplying by LCD, c
x - cx = ac - bc
x(1 - c) = ac - bc
{{{highlight_green(matrix(1,3, x = (ac - bc)/(1 - c), or, x = c(a - b)/(1 - c)))}}}