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)
