Question 77944
To solve this system by the addition method, we simply add the 2 equations. However, we want to eliminate a variable (lets choose x), so we must multiply the top equation by 2

<pre>


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

</pre>

Distribute the 2

<pre>


     10x – 6y =  6
    -10x + 6y = -4

</pre>

Now add the like terms of the 2 equations. For instance we'll add 10x and -10x to get {{{10x+(-10x)=0x}}}. Do this for every like term

<pre>


    (10x+(-10x)) + (6y+(-6y)) = 6+(-4)

</pre>

<pre>


    0x + 0y = 2

</pre>

So we get

<pre>


    0=2

</pre>

which is not true. So this means for any x we choose, this system will never be satisfied. So there are no solutions