SOLUTION: i need help with- x+y=9 y=2x when the directions say solve by graphing and substitution thank you

Question 173516: i need help with-
x+y=9
y=2x when the directions say solve by graphing and substitution
thank you
Answer by gonzo(654) (Show Source): You can put this solution on YOUR website!
you have 2 equations:
x+y = 9
y = 2x
-----
since y = 2x in the second equation, you substitute 2x for y in the first equation to get:
-----
x + 2x = 9
simplify to get:
3x = 9
divide both sides by 3 to get:
x = 9/3 = 3
-----
since x = 3, take any equation and solve for y.
second equation says y = 2x
since x = 3,
y = 2*3 = 6
-----
since x = 3 and y = 6, plug these values into the first equation to get:
x + y = 9
3 + 6 = 9
9 = 9
equation is true so values of x = 3 and y = 6 are good.
graph of these equations should show the intersection of the 2 lines at the point (x,y) = (3,6)
in order to graph these equations, make them so that y is on the left hand side of the equation and x is on the right hand side of the equation (solve for y in both equations).
second equation is already there:
y = 2x
first equation needs to be manipulated:
x + y = 9
subtract x from both sides of the equation to get:
y = 9-x
first equation is now in the right form.
both equations that are in graphing form are:
y = 2x
y = 9-x
-----
here's a graph of the equations:

you can see that these lines intersect at the point (3,6) which is exacty the point we calculated them to be when we solved both equations simultaneously.
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