What is 2x +4y=0 when y =-8x?

Question

What is 2x +4y=0 when y =-8x?

Answer 1

Hi Amber, there are two ways of going about this problem:

 

 

Method I

 

2x +4y=0 -- Equation 1

y =-8x -- Equation 2

 

 

Multiply the first equation by -4 to get the "x" coefficient of "2" equal to -8.

 

-4 * (2x + 4y) = 0 

 

-8x - 16y = 0

 

 

Now substitute in "y" for the "-8x" in the second equation to get:

 

 

y - 15y = 0

 

 

Combine like terms and solve for 'y':

 

 

-14y = 0

 

y = 0

 

 

Now, plug your value for 'y' back into either of the two equations above and solve for 'x':

 

 

y = -8x

 

0 = -8x

 

x = 0

 

 

 

Method II

 

2x +4y=0 -- Equation 1
y =-8x -- Equation 2

 

 

Another way of doing this is simply plugging in '-8x' for 'y' from the second equation into the first equation as follows:

 

 

2x + 4 * (-8x) = 0

 

2x + (-32x) = 0

 

-30x = 0

 

x = 0

 

 

Take your value for 'x' and plug it into either of the two equations to solve for 'y':

 

 

y = -8x

y = -8 * (0)

 

y = 0

Answer 2

What we have here is a substitution problem. Let's put -8x into y:

2x + 4(-8x) = 0

2x - 32x = 0

-30x = 0

x = 0

 

Let's try another method to verify our answer there. This time isolating y in 2x + 4y = 0:

4y = -2x

y = -¹/₂ x

 

Since they both equal y, they equal one another:

-8x = -¹/₂ x

-¹⁶/₂ x = -¹/₂ x

-¹⁵/₂ x = 0

x = 0

 

So x is indeed 0. Let's put that into our equations:

2 * 0 + 4y = 0

0 + 4y = 0

4y = 0

y = 0

 

y = -8 * 0

y = 0