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

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)
RELATED QUESTIONS
Solve the following system of linear equations using either the substitution method or... (answered by rothauserc)

solve and check the system of equations using either substitution or addition method.... (answered by Fombitz)

Solve the system of linear equations using addition/subtraction method. 2x+y=3... (answered by padejr)

Solve the system of linear equations using addition/subtraction method: 2x+y=3... (answered by jim_thompson5910)

solve each system using the substitution method or the addition method 3(2x+y)=4x+20... (answered by mananth)

Solve the system of linear equations using substitution method: 2x+3y=5... (answered by jim_thompson5910)

4) Solve the system of equations using the substitution method 5x + 2y = 4 and 3x + y (answered by stanbon)

Solve the following system of equations using either the substitution method or the... (answered by MathLover1)

Solve the system of linear equations using the Substitution Method. x+2y=3... (answered by haileytucki)