SOLUTION: I have to solve & define these problems and determine if it's independence or independent, consistent or inconsistent then graph them but I don't know how. 4x+2y=4 16x+8y=16

Algebra ->  Graphs -> SOLUTION: I have to solve & define these problems and determine if it's independence or independent, consistent or inconsistent then graph them but I don't know how. 4x+2y=4 16x+8y=16       Log On


   

Question 141986This question is from textbook cord algebra 1 part B
: I have to solve & define these problems and determine if it's independence or independent, consistent or inconsistent then graph them but I don't know how.
4x+2y=4
16x+8y=16
y= -3x
y= -2x+1
thank you This question is from textbook cord algebra 1 part B

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do the first one to get you started

Let's solve this system by use of elimination/addition.


Start with the given system of equations:

system%284x%2B2y=4%2C16x%2B8y=16%29



Now in order to solve this system by using elimination/addition, we need to solve (or isolate) one variable. I'm going to solve for y.





In order to solve for one variable, we must eliminate the other variable. So if we wanted to solve for y, we would have to eliminate x (or vice versa).


So lets eliminate x. In order to do that, we need to have both x coefficients that are equal in magnitude but have opposite signs (for instance 2 and -2 are equal in magnitude but have opposite signs). This way they will add to zero. By adding to zero, they can be eliminated.



So to make the x coefficients equal in magnitude but opposite in sign, we need to multiply both x coefficients by some number to get them to an common number. So if we wanted to get 4 and 16 to some equal number, we could try to get them to the LCM.



Since the LCM of 4 and 16 is 16, we need to multiply both sides of the top equation by 4 and multiply both sides of the bottom equation by -1 like this:




4%284x%2B2y%29=4%284%29 Multiply the top equation (both sides) by 4
-1%2816x%2B8y%29=-1%2816%29 Multiply the bottom equation (both sides) by -1




Distribute and multiply

16x%2B8y=16
-16x-8y=-16


Now add the equations together. In order to add 2 equations, group like terms and combine them

%2816x-16x%29%2B%288y-8y%29=16-16

Combine like terms and simplify



cross%2816x-16x%29%2B0y=0 Notice how the x terms cancel out



0=0 Simplify

Since this equation is always true regardless of what x or y is, we have an infinite number of solutions. So this system is dependent (ie one equation is dependent on the other). Also, because we have an infinite amount of solutions, this means that the system is consistent.

Notice that if we graph the two equations we get

graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+%284-4x%29%2F2%2C+%2816-16x%29%2F8%29+ Graph of 4x%2B2y=4 and 16x%2B8y=16(one graph is on top of the other).