Question 747319
I prefer to use elimination.  Here's how it goes.

You need to get either both x coefficients to be the same or both y's to be the same.  Multiplying the top equation by two would result in the x coefficients being the same.


So, multiplying the first equation by 2 gives you:

{{{4x+2y=10}}} 

Now you need to line up the two equations like you would a subtraction problem.  We will be subtracting one equation from the other to eliminate the x's.

{{{4x+2y=10}}} 
minus
{{{4x+3y=14}}} 

Note:(As I'm new to the site, I'm not sure how to write this step best yet so I had to write the word minus rather than having them lined up one under the other and just having a minus sign off to the side to show that you'll be subtracting.)

So 4x-4x=0 so the x's have been eliminated.  

2y-3y=-y and 10-14=-4

Since the x's were eliminated, you're left with:

{{{-y=-4}}}

 Multiply or divide both sides by negative one to get:

{{{y=4}}} 

Now, simply plug in your value for y into any equation from the problem.  
I'll use,

{{{2x+y=5}}} 

Plugging in 4 for y gives you

{{{2x+4=5}}} 

Subtract 4 from both sides

{{{2x=1}}} 

Divide both sides by 2

{{{x=1/2}}}

Now you have both x and y so your solution is the ordered pair (1/2,4)