SOLUTION: After graphing 4x-2y=5 and y=x how many points do they intersect?

Question 285593: After graphing 4x-2y=5 and y=x how many points do they intersect?
Found 2 solutions by Alan3354, toidayma:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
1
They're straight lines, and their slopes are not equal.
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Answer by toidayma(44) (Show Source): You can put this solution on YOUR website!
Well, there are several ways to answer this question:
1> After graphing it, you will see that there will be one point intersected.
2> Looking at the two equations, these are equations of straight line, since the slopes are different (look at the coefficients of x/coefficient of y in the equations) thus, they intersect at one point only.
By the way, if the two slopes are equal, they may be parallel and have no common point or the two line are one i.e. they have indefinite common points.
3> Let (xo, yo) the common point of the two lines, since the point belong to both line, the coordinates have to satisfy both the equations -> Solve the system of equations. The number of combination (xo,yo) are the number of point they have in common i.e the number of point they intersect.
(1) 4xo - 2yo = 5
(2) yo = xo
From (2), substitute y by x in the equation (1), we have: 4xo - 2xo = 5 <-> xo = 2.5, look back at (2) -> yo = xo = 2.5, so there is only one common point (2.5,2.5).
If you have any more questions on this problem, send me a message.
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