Question

What is the solution of this linear system? x+y=13

Answer 1

Answer:

The solution of the linear equation is: (6,7)

Step-by-step explanation:

This being that:

x + y = 13

1/2x + y = 10

What you do in order to find the solution is either (2 ways):

- Substitution

- Elimination

I'm sure that either way, you'll get the same thing. I used: Substitution.

To do this choose either if you want to find [x] or [y] first, then substitute it in. I will choose to find [x] first.

x + y = 13

          - y    

x = 13 - y

Now substitute it into:  

1/2x + y = 10

1/2(13 - y) + y = 10

1/2(13 -y) + y= 10

Then to get rid of fraction, instead of dividing, you multiply with reciprocal

1/2 · 2/1 (They cancel out) Leaving you with:

(13 - y) 2(y) = 2(10)

(Everything is multiplied, except for 13 - y, because it had parenthesis to protect it.)

13 - y + 2y = 20

13 + y = 20

- 13       - 13

          y = 7

You now have your [y] for your coordinate.

(x, 7), now time to find your [x]

Now you substitute your [y] into your equation:

1/2x + (7) = 10

1/2x + 7 = 10

         -7 = -7

1/2x = 3

(To get rid of fraction, multiply on both sides with reciprocal)

1/2 cancels out with 2/1

x = 2(3)

x = 6

You now have your [x] coordinate.

This is your coordinate:

(6,7)