SOLUTION: 3x+y=0 x+y=2 I'm not exactly sure on what catergory this falls under, but I don't understand the problem and basically what I'm doing.

Question 82177: 3x+y=0
x+y=2

I'm not exactly sure on what catergory this falls under, but I don't understand the problem and basically what I'm doing.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
If you want to solve this system by substitution then...

Solved by pluggable solver: Solving a linear system of equations by subsitution

Lets start with the given system of linear equations

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

Solve for y for the first equation

Subtract from both sides

Divide both sides by 1.

Which breaks down and reduces to

Now we've fully isolated y

Since y equals we can substitute the expression into y of the 2nd equation. This will eliminate y so we can solve for x.

Replace y with . Since this eliminates y, we can now solve for x.

Distribute 1 to

Multiply

Reduce any fractions

Add to both sides

Combine the terms on the right side

Now combine the terms on the left side.

Multiply both sides by . This will cancel out and isolate x

So when we multiply and (and simplify) we get

<---------------------------------One answer

Now that we know that , lets substitute that in for x to solve for y

Plug in into the 2nd equation

Multiply

Add to both sides

Combine the terms on the right side

Multiply both sides by . This will cancel out 1 on the left side.

Multiply the terms on the right side

Reduce

So this is the other answer

<---------------------------------Other answer

So our solution is

and

which can also look like

(,)

Notice if we graph the equations (if you need help with graphing, check out this solver)

we get

graph of (red) and (green) (hint: you may have to solve for y to graph these) intersecting at the blue circle.

and we can see that the two equations intersect at (,). This verifies our answer.

-----------------------------------------------------------------------------------------------
Check:

Plug in (,) into the system of equations

Let and . Now plug those values into the equation

Plug in and

Multiply

Add

Reduce. Since this equation is true the solution works.

So the solution (,) satisfies

Let and . Now plug those values into the equation

Plug in and

Multiply

Add

Reduce. Since this equation is true the solution works.

So the solution (,) satisfies

Since the solution (,) satisfies the system of equations

this verifies our answer.

Or if you want to solve by elimination:

Solved by pluggable solver: Linear Systems by Addition

We'll solve the system:

by elimination by addition.To eliminate by addition, we need to set both coefficients of x to numbers with changed signs, i.e a and -a. Since in the second equation we have 1 as our coefficient for x, to get -3 we have to multiply all terms of the second equation by which is equal to -3.

Multiplying, we get on our second equation:

Adding both equations we get:

Since 3 and -3 cancel out, we have a linear equation:Therefore, we know that y = 3.

Plugging that in into the first equation gives us:

Therefore, our answer is:

Whatever method you choose, you'll get the same answer (provided you did it right of course).
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