How is this problem laid out
Answer:
(- 3, 37) and (-
,
)
Step-by-step explanation:
Given the 2 equations
2x² - y + 19 = 0 → (1)
y + 11x = 4 → (2) ← subtract 11x from both sides
y = 4 - 11x → (3)
Substitute y = 4 - 11x into (1)
2x² - (4 - 11x) + 19 = 0
2x² - 4 + 11x + 19 = 0
2x² + 11x + 15 = 0 ← in standard form
(2x + 5)(x + 3) = 0 ← in factored form
Equate each factor to zero and solve for x
2x + 5 = 0 ⇒ 2x = - 5 ⇒ x = - 
x + 3 = 0 ⇒ x = - 3
Substitute these values into (3) for corresponding values of y
x = -
: y = 4 +
=
⇒ (-
,
)
x = - 3 : y = 4 + 33 = 37 ⇒ (- 3, 37 )
Multiply the first equation by -2. It turns into 4x+18y=50 and the other one stays -4x-9y=-23. Then you "eliminate" the equations by "adding" them. Set it up like this:
4x+18y=50
+
-4x-9y=-23
4x-4x= 0. 18y-9y= 9y and 50-23= 27
SO: 9y= 27 and y= 3
And then you plug that in to one equation: 4x +18(3)= 50. 4x= 50-(18*3)
4x= -4, so x=-1.
Plug it back in to check!
Hope this helps. Happy solving! :)
You are being asked to make π the subject in

So divide both sides of the equation by

That is

The you have

or

I hope this is helpful?
The lines would go up and over at the same rate. They would have the same slope, like parallel lines.
Hope this helps!! :)