Given: ax+by=d and y=mx+c. Find x in terms of a,b,c,d and m.
We want to isolate x in terms of the other variables.
One way to do this is to first add the two equations:
`ax + by = d`
`y = mx + c rarr -mx + y = c`
Adding the two equations gives us:
`ax - mx + by + y = c + d`
Which can be re-expressed as
`(a-m)x + (b+1)y = c + d`
Now, we isolate x.
First, move all terms without an x to the other side.
`(a-m)x = c + d - (b+1)y`
Then, divide both sides by (a - m), the coefficient of x:
`x = (c+d-(b+1)y)/(a-m)`
`x = (c+d-by-y)/(a-m)`