SOLUTION: What is the value of x in the solution to the system of equations below? 6x + 3y = 13 3x - y = 4 1 (5/3) (8/3) (7/3) I got 1

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Question 1034035: What is the value of x in the solution to the system of equations below?
6x + 3y = 13
3x - y = 4
1
(5/3)
(8/3)
(7/3)
I got 1
Found 2 solutions by algebrapro18, MathTherapy:
Answer by algebrapro18(249)   (Show Source): You can put this solution on YOUR website!
There are two ways we can do this. We can either solve it using substitution or elimination. I will do both.

Solving using Substitution:


To solve the system using substitution we need to solve one of the equations for y. Since the second equation has y with no number(coefficant) in front of it we can solve that equation for y easily.



3x - y = 4 Subtract 3x from both sides
-y = 4-3x Divide by -1
y = -4+3x



Now that we have an expression for y we can substitute(hence the name of the method) that into the first equation and solve for x.



6x + 3y = 13 Substitute 4+3x in for y
6x + 3(-4+3x) = 13 Distribute the 3
6x - 12 + 9x = 13 Combine Like terms
15x - 12 = 13 Add 12 to both sides
15x = 25 Divide both sides by 15
x = 25/15 Simplify the fraction
x = 5/3



Solving using Elimination:
To solve the system using elimination we need to eliminate a varable. Since your question specifically asks what the value of x is we should eliminate y. To do this we multiply both sides of the bottom equation by 3 and add the two equations together.

3(3x - y) = 3(4) Distribute
9x-3y = 3(4) Multiply on the right
9x-3y = 12

Adding our equations together we get
6x+3y=13
9x-3y=12
---------
15x = 25

Now we can solve the equation for x by dividing both sides by 15. Simplifying our answer we get the same 5/3 we got above.

Answer by MathTherapy(10556)   (Show Source): You can put this solution on YOUR website!

What is the value of x in the solution to the system of equations below?
6x + 3y = 13
3x - y = 4
1
(5/3)
(8/3)
(7/3)
I got 1 
MULTIPLY eq (ii) by 3. This will give you: 9x - 3y = 12 ----- eq (iii)

Now you can ADD eqs (iii) & (i) to find x. You will get 15x = 25. . That much is known! 

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