I have to solve this equation with the dependent system. The text book doesn't go into much info?

Question

and I tried to look it up online, but nothing helped. So if someone can point me in the general direction that would be great. I'm not asking for the answer just help, so if you use a different example thats great. the example we were given in the book is x - 2y = 8 and 3x -2y = 12.

Answer 1

x = 8 + 2y
plug in other eqn:
3(8+2y) - 2y = 12
= 24 + 6y - 2y = 12
= 4y = -12
y = -3

Plug in to first eqn:
x - (2*-3) = 8
= x - (-6) = 8
x + 6 = 8
x = 2

Answer 2

The dependant system is simply solving one of the equations whereby one unknown value, say y, is dependant on the value of the other variable. And then substitute this value for y in the other equation and solving for x.

For example, x-2y=8
-2y=8-x
y=-4+x/2

substitute this value of y into the other equation.

3x-2y=12
3x-2(-4+x/2)=12
3x+8-x=12
2x=4
x=2

Now, substitue this value for x into x-2y=8 and solve for y.

Answer 3

Write this as:
2y = x - 8 and 2y = 3x - 12
y = x/2 - 4 and y = 3x/2 - 6

Dependency means that for every x there is only one y. Both of these are dependent equations. X causes y.

Answer 4

Let's use substitution. Solve equation (1) for x:

x - 2y = 8
x = 2y + 8

Plug into equation 2:

3x - 2y = 12
3(2y + 8) - 2y = 12
6y + 24 - 2y = 12
4y = 12 - 24
4y = -12
y = -3

Plug back in to equation (1):

x - 2(-3) = 8
x + 6 = 8
x = 2

Answer 5

Hi,

Dependent system could mean y is dependent on x or x is dependent on y.

So calculate the value of y in terms of x using eqn 1 and substitute the result in eqn2 to get the value of x and from that calculate y

Good luck