Method of Elimination

Question

Okay so I know how to do this where you have to cancel one of the variables out to solve for one then plug it back in and solve for the other. But I have no equations and they both came out to 0=0 I think and I don't know if I did this right or if that means there are no solutions or infinite solutions because I know that is possible.

The first one has a system of 0.02x-0.04y=0.08 and

                                           x-2y=4

so I multiplied the first equation by -50 so it was -x+2y=-4 and I went to go add that together with the second equation and I got 0=0.

The second one has a system of 0.05x+0.1y=0.6 and

                                               x+2y=12

so once again I multiplied the first equation by -20 and it was -x-2y=-12 and I added it with the second equation and got 0=0 again.

I don't know if I am setting the problems up wrong of if they are actually turning out to be 0=0? Please help!!

Answer 1

Kari,

 

You had an error in your arithmetic.

 

EQ#!:   0.02x - 0.04y = 0.08 becomes  x -  2y = +4  when divided by 0.02 on both sides of = sign.

EQ#2:  0.05x +  0.1y = 0.6  becomes   x + 2y = 6/5 when divided by 0.05 on both sides of = sign.

 

Adding these equations, you get 2x + 0y = 4 + 5/5 = +26/5, so x = + 13/5

And using EQ#2,  y = +6/10 - 13/10 = - 7/10

 

To check this solution plug x = +13/5 and y = -7/10 into EQ#1 and EQ#2 and see that they balance.

Answer 2

You did these correctly.

If you're given two equations that are essentially the same equation, it means they are infinite solutions.

Let's look at the first set. Let's say you multiplied .02x-.04y=.08 by 50 (instead of -50).

You'd get x-2y=4.

But wait! That's the same as second equation!

That means any combination of x and y will work.

 

For example, (0,-2),(4,0),(114,55)... Any point that satisfies the first equation also satisfies the second equation because they are the same equation.

 

https://www.desmos.com/calculator

Type in your two equations into this graphing calculator. You will see that they are the same line. [Infinite solution]

 

Usually, two lines cross at a single point, which is how you get your 1 solution. [1 solution]

 

Now what about No Solution? What would two lines that never cross look like?