[SPLIT] solve system y = -2x, 2x + y = 6 by graphing

[bjusreal]

y = -2x
2x + y = 6

My choices are 1. (2,6) 2. no solution 3. (0,0) 4. Infinite number of solutions.

I'm unsure on how to solve this problem:

I first tried to take -2 (x-y = -2x)

-2x +2y = -4x
2x + y = 6
_____________
3y = 2x (I'm stuck)

 

[Denis]

Re: Extra Credit System Of Equations

Please start your own thread.

 

[mmm4444bot]

y = -2x
2x + y = 6

My choices are 1. (2,6) 2. no solution 3. (0,0) 4. Infinite number of solutions.

I first tried to take -2 (x-y = -2x)

We don't substitute an equation for x in y = -2x.

Instead, we solve one of the two given equations for x, and then we substitute that result for x in the other equation.

There is more than one approach.

Since you tried to substitute for x in the equation y = -2x, let's first solve the other equation for x. (I'll show you an alternate method, at the end of this post.)

2x + y = 6

x = (6 - y)/2

Now, substitute the expression (6 - y)/2 for x in the equation y = -2x.

That will give you an equation that contains only the variable y.

Simplify this equation, and the answer will become obvious.

ALTERNATE METHOD:

You might find this approach easier.

We already have an expression for y; it's -2x, right?

I mean, we're told that y is the same number as -2x.

So, substitute the expression -2x for y in the other equation, and simplfy.

Again, the answer will become obvious.

Cheers ~ Mark

PS: Denis is right; you've inserted your request for help into somebody else's discussion.

Please click the [NEWTOPIC] button, to start your own discussions.

 

[Denis]

Re:

PS: Denis is right;

Nope; I'm a southpaw :roll:

 

[wjm11]

Re: Extra Credit System Of Equations

w+x+y+z = 2
2w-x-y+2z = 7
2w+3x+2y-z = -2
3w-2x-y-3z = -2

Mallory, this won’t give you the steps, but it will give you something to shoot for. Solution:

W = 1
X = 0
Y = -1
Z = 2

(But perhaps you already knew that…) Of course, once you solve, you’d plug your answers in to make sure anyway.

I’m not sure what methods you’ve been taught, but setting the problem up in matrix form and using the Gaussian elimination method is a good way to go. It’s a little tedious, but the steps are straightforward. You could try Googling it if you’re curious/ambitious.