Given: ax+by=d and y=mx+c. Find x in terms of a,b,c,d and m.

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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)`

or

`x = (c+d-by-y)/(a-m)`

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