What is the solution of this linear system? x+y=13
1/2x+y=10

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 reciprocal1/2 · 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 = 2013 + y = 20- 13       - 13           y = 7You 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 = -71/2x = 3(To get rid of fraction, multiply on both sides with reciprocal)1/2 cancels out with 2/1x = 2(3)x = 6You now have your [x] coordinate.This is your coordinate: (6,7)

 

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