1. ## simultaneous system

Hi everyone, new to this site! I have a homework question that I am stumped on. I am trying to solve the system by elimation.

x + y = 5
and
x - y = 1

I can solve by substitution, but by elimation confuses me. Can anyone help??

Thanks!

2. Using elimination means that you add an ENTIRE FUNCTION to another one, you do this by adding each individual term, to arrive at an equality of one term, then you use back-substitution to finish the problem:

You have:

$\displaystyle x + y = 5$

and

$\displaystyle x - y = 1$

Notice, you have a positive and a negative y, let's add these two together and see what we come up with:

$\displaystyle x + y = 5$
$\displaystyle x - y = 1$

Now we just add each set of terms, starting with the x's:

$\displaystyle x + x = 2x$

Next, the y's:

$\displaystyle y - y = 0$ <--- Just got rid of the y's

Next, the constants:

$\displaystyle 5 + 1 = 6$

Now, we construct a new equation:

$\displaystyle 2x + 0 = 6$

Solve for x:

$\displaystyle x = 3$

Now, we have to find a y:

$\displaystyle x + y = 5$

$\displaystyle 3 + y = 5$

$\displaystyle y = 2$

All we do, is check the OTHER equation for validity:

$\displaystyle x - y = 1$

$\displaystyle 3 - 2 = 1$

That is true, so it works.

3. x + y = 5
x - y = 1

To solve a system of linear equations by elimination, you are trying to eliminate one of the variables by adding or subtracting the 2 equations.

Here, simply add the 2 equations together to eliminate y.

2x = 6
x = 3

Substitute x = 3 into the first equation:
3 + y = 5
y = 2

Try this site: Systems of Equations - Solve by addition or subtraction