how do you find the point of intersection ?

Question

owlfred · Answer

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anonymous · Answer

point of intersection of what?

anonymous · Answer

on a graph
but without seeing the graph

anonymous · Answer

yes, but what are you drawing on the graph? straight lines? circles? ellipses? exponential curves?

anonymous · Answer

linear relations.....

anonymous · Answer

okay. so, do you have equations of the two lines?

anonymous · Answer

yes

anonymous · Answer

post them

anonymous · Answer

one second

anonymous · Answer

$$y=-2x+7$$

anonymous · Answer

$$y=3x-8$$

anonymous · Answer

okay. so, we have two equations. now, to find the point of intersection we need to find what is called a "solution" to the given set of equations

anonymous · Answer

there are a number of ways to "solve" these equations. you can try out combinations of numbers and see which combinations satisfy both the equations. This is generally too hard. there could be millions of combinations. trial and error is not a a very good method.

myininaya · Answer

you want to find when they are the same (so set them equal to on another to when this happens)
-2x+7=3x-8 solve for x

anonymous · Answer

the next method is called substitution.
you take y = -2x+7 and substitute this value of y into the other equation
so -2x+7 = 3x -8
add 2x to both sides and add 8 to both sides
5x = 15, x = 3
now, x = 3
to find the corresponding y value, substutute this value of x in any of the two equations
-2(3)+7 = y which means y = 1

anonymous · Answer

so (3,1) is the point of intersection of the two lines.

myininaya · Answer

gj dhartraditya :)

anonymous · Answer

thank you :)

anonymous · Answer

There is one more method. it is called elimination
y = -2x +7 ---- equation 1
y = 3x -8 ------- equation 2
subtract equation 1 from equation 2, since we notice that if we subtract one equation from the other, the variable y will cancel itself out, or will be "eliminated".
this means y - y = 3x-8-(-2x+7)
0= 5x-15
x =3 and so on.

anonymous · Answer

thanks myininaya :)