Answer:
(a) x = -2y
(c) 3x - 2y = 0
Step-by-step explanation:
You can tell if an equation is a direct variation equation if it can be written in the format y = kx.
Note that there is no addition and subtraction in this equation.
Let's put these equations in the form y = kx.
(a) x = -2y
- y = x/-2 → y = -1/2x
- This is equivalent to multiplying x by -1/2, so this is an example of direct variation.
(b) x + 2y = 12
- 2y = 12 - x
- y = 6 - 1/2x
- This is not in the form y = kx since we are adding 6 to -1/2x. Therefore, this is <u>NOT</u> an example of direct variation.
(c) 3x - 2y = 0
- -2y = -3x
- y = 3/2x
- This follows the format of y = kx, so it is an example of direct variation.
(d) 5x² + y = 0
- y = -5x²
- This is not in the form of y = kx, so it is <u>NOT</u> an example of direct variation.
(e) y = 0.3x + 1.6
- 1.6 is being added to 0.3x, so it is <u>NOT</u> an example of direct variation.
(f) y - 2 = x
- y = x + 2
- 2 is being added to x, so it is <u>NOT</u> an example of direct variation.
The following equations are examples of direct variation:
Answer:
27
Step-by-step explanation:
19+22+46+24+37+16+19+33=216
216/8=27
Start by writing the system down, I will use 
to represent 
Substitute the fact that 
into the first equation to get,
Simplify into a quadratic form (
),
Now you can use Vieta's rule which states that any quadratic equation can be written in the following form,
which then must factor into
And the solutions will be 
.
Clearly for small coefficients like ours 
, this is very easy to figure out. To get 5 and 6 we simply say that 
.
This fits the definition as 
and 
.
So as mentioned, solutions will equal to but these are just x-values in the solution pairs of a form 
.
To get y-values we must substitute 3 for x in the original equation and then also 2 for x in the original equation. Luckily we already know that substituting either of the two numbers yields a zero.
So the solution pairs are 
and 
.
Hope this helps :)
Answer:
he will be 17 in
Step-by-step explanation:
