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
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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