Question 329392
Show me how to use elimination to solve the system of equations given by
3x-2y=10 and 5x+2y=6. Thanks
<pre><b>

Draw a line underneath:

<font color = "red">3x</font><font color = "green">-2y</font>=10 
<font color = "red">5x</font><font color = "green">+2y</font>= 6
--------

Add the red <font color = "red">3x</font> to the red <font color = "red">5x</font>.  That gives <font color = "red">8x</font>.  Write that down below the line.

<font color = "red">3x</font><font color = "green">-2y</font>=10 
<font color = "red">5x</font><font color = "green">+2y</font>= 6
--------
<font color = "red">8x</font>

Add the green <font color = "green">-2y</font> to the green <font color = "green">+2y</font>.  But they just cancel out because they are
just alike except one has a - before it and the other has a +
before it:


<font color = "red">3x</font><s><font color = "green">-2y</font></s>=10 
<font color = "red">5x</font><s><font color = "green">+2y</font></s>= 6
--------
<font color = "red">8x</font>

Next bring down the equal sign

<font color = "red">3x</font><s><font color = "green">-2y</font></s>=10 
<font color = "red">5x</font><s><font color = "green">+2y</font></s>= 6
--------
<font color = "red">8x</font>   =

Now add the 10 and the 6 getting 16. Write that down:

<font color = "red">3x</font><s><font color = "green">-2y</font></s>=10 
<font color = "red">5x</font><s><font color = "green">+2y</font></s>= 6
--------
<font color = "red">8x</font>   =16

Now you have the equation

{{{8x}}}{{{""=""}}}{{{16}}}

Divide both sides by 8:

{{{8x/8}}}{{{""=""}}}{{{16/8}}}

{{{cross(8)x/cross(8)}}}{{{""=""}}}{{{16/8}}}

x = 2

Go back to one of the original equations:

3x-2y=10

In place of x, substitute (2)

3(2)-2y=10

Multiply the 3 by the 2 getting 6

   6-2y=10

Add -6 to both sides:

   6-2y=10
  -6    -6
  --------
    -2y= 4

Now we have the equation:

{{{-2y=4}}}

We divide both sides by -2

{{{(-2y)/(-2)=4/(-2)}}}

{{{(cross(-2)y)/cross(-2)=-2}}}

y = -2

So the solution is (x,y) = (2,-2)

To check we substitute (2) for x and (-2) for y in each equation

     3x-2y=10 and      5x+2y=6
3(2)-2(-2)=10 and 5(2)+2(-2)=6
       6+4=10 and       10-4=6
        10=10 and          6=6

So the solution is correct.

Edwin</pre>