SOLUTION: 1. Solve the following system of linear equations using either the substitution method or the addition method: 2x+y=5 4x+3y=14 Please help me solve this problems and each st

Click here to see ALL problems on test

Question 747319: 1. Solve the following system of linear equations using either the substitution method or the addition method:
2x+y=5
4x+3y=14
Please help me solve this problems and each step in order to understand it.
Thank you in advance.
Answer by timvanswearingen(106) (Show Source):
You can put this solution on YOUR website!
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:

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.

minus

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:

Multiply or divide both sides by negative one to get:

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

Plugging in 4 for y gives you

Subtract 4 from both sides

Divide both sides by 2

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