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I have a question on my homework that I have no idea how to solve. Speedy help would be appreciated.
Where do the lines Y=ax+b and Y=cx+d cross, assuming that a, b, c, and d are integers and a is not equal to c?
I know how to solve it when a,b,c, and d are integers, but here I'm lost. If you solve it the same way you get that x=(d-b)/(a-c) and how do you get Y?
Originally posted by clandarkfirelook......make sure you think about this.
I have a question on my homework that I have no idea how to solve. Speedy help would be appreciated.
Where do the lines Y=ax+b and Y=cx+d cross, assuming that a, b, c, and d are integers and a is not equal to c?
the place where the lines intersect (cross) is where the above functions of the variable "x" are equal
so for the "x" coordinate of the point of intersection solve the following equation for "x"
ax+b=cx+d
just treat the letters as numbers ( because that is what they represent )
your first step is to group like terms ( ie get all the terms involed with "x" one side, and then group the constants b and d on the other.
then factor out the "x" and get it alone by division.
now you have the solution for the x coordinate in a general form.
hope this helps...
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Originally posted by clandarkfireto the last part of your question
I have a question on my homework that I have no idea how to solve. Speedy help would be appreciated.
Where do the lines Y=ax+b and Y=cx+d cross, assuming that a, b, c, and d are integers and a is not equal to c?
I know how to solve it when a,b,c, and d are integers, but here I'm lost. If you solve it the same way you get that x=(d-b)/(a-c) and how do you get Y?
by substitution you get "Y"
you sustitute your general solution for "x" into either one of the original equations
so
Y = a(d-b)/(a-c) + b
or
y = c(d-b)/(a-c) + d
both are correct