Question

Hi! Can someone help me with this? Thanks!


Directions: Solve this equation by doing it twice; one time using the substitution method and one time using the graphing method.

x – 2y = 0
3x – y^2 = 0

Answer 1

Substitution method:

x – 2 y = 0 Add 2 y to both sides

x – 2 y + 2 y = 0 + 2 y

x = 2 y


3 x – y ^ 2 = 0

3 * 2 y - y ^ 2 = 0

6 y - y ^ 2 = 0

- y ^ 2 + 6 y = 0 Multiply both sides by - 1

y ^ 2 - 6 y = 0

y * y - 6 y = 0

y * ( y - 6 ) = 0


Obviously solution y = 0

and

y - 6 = 0 Add 6 to both sides

y - 6 + 6 = 0 + 6

y = 6


Now put this solutions in eguation :

x = 2 y


For y = 0

x = 2 y

x = 2 * 0 = 0


For y = 6

x = 2 y

x = 2 * 6 = 12


The solutions are :

x = 0 , y = 0

and

x = 12 , y = 6

You can write this like :

( 0 , 0 ) and ( 12 , 6 )



For graph :

In google type :

functions graphs online

When you see list of results click on :

rechneronline.de/function-graphs/


When page be open in blue rectangle type :

x / 2

In first gray rectangle type :

( 3 x ) ^ ( 1 / 2 )

In second gray rectangle type :

- ( 3 x ) ^ ( 1 / 2 )


Set :

Range x-axis from - 4 to 16

Range y-axis from - 4 to 16

and click option:

Draw


You will see graphical solution.

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Remark :

If x = 2 y

then y = x / 2


and

3 x – y ^ 2 = 0

is same :

y ^ 2 = 3 x


y = + OR - sqrt ( 3 x )

y = + OR - ( 3 x ) ^ ( 1 / 2 )



y = ( 3 x ) ^ ( 1 / 2 )

and

y = - ( 3 x ) ^ ( 1 / 2 )

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