Use the substitution method to solve this system of equations. Choose the correct ordered pair. 2x-y=10. 2x-2y=4
2 answers:
Answer:
(x, y) = (8, 6)
Step-by-step explanation:
given the 2 equations
2x - y = 10 → (1)
2x - 2y = 4 → (2)
rearrange equation (1) expressing y in terms of x
y = 2x - 10 → (3)
Substitute y = 2x - 10 in equation (2)
2x - 2(2x - 10) = 4
2x - 4x + 20 = 4
- 2x + 20 = 4 ( subtract 20 from both sides )
- 2x = - 16 ( divide both sides by - 2 )
x = 8
substitute x = 8 in equation (3)
y = (2 × 8) - 10 = 16 - 10 = 6
solution is (8 , 6)
ANSWER
The correct ordered pair is
![(8,6).](https://tex.z-dn.net/?f=%288%2C6%29.)
EXPLANATION
The given equations are
![2x - y = 10](https://tex.z-dn.net/?f=2x%20%20-%20y%20%3D%2010)
We make y the subject and call it equation (1).
Thus,
![- y = - 2x + 10](https://tex.z-dn.net/?f=%20-%20y%20%3D%20-%202x%20%2B%2010)
This implies that,
![y = 2x - 10 - - - (1)](https://tex.z-dn.net/?f=y%20%3D%202x%20-%2010%20-%20%20-%20-%20%20%281%29)
The second equation is
![2x - 2y = 4 - - - (2)](https://tex.z-dn.net/?f=2x%20-%202y%20%3D%204%20-%20%20-%20%20-%20%282%29)
We substitute equation (1) into equation (2).
![2x - 2(2x - 10) = 4](https://tex.z-dn.net/?f=2x%20-%202%282x%20-%2010%29%20%3D%204)
We expand brackets to obtain,
![2x - 4x + 20 = 4](https://tex.z-dn.net/?f=2x%20-%204x%20%20%2B%2020%20%3D%204)
This implies that,
![2x - 4x= 4 - 20](https://tex.z-dn.net/?f=2x%20%20-%204x%3D%204%20-%2020)
![- 2x = - 16](https://tex.z-dn.net/?f=%20-%202x%20%3D%20%20-%2016)
![x = 8](https://tex.z-dn.net/?f=x%20%3D%208)
We put this value in to equation (1) to get,
![y = 2(8) - 10](https://tex.z-dn.net/?f=y%20%3D%202%288%29%20-%2010)
![y = 16 - 10](https://tex.z-dn.net/?f=y%20%3D%2016%20-%2010)
![y = 6](https://tex.z-dn.net/?f=y%20%3D%206)
The correct orders pair is
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