Answer:
The correct ordered pair is (7,1)
Step-by-step explanation:
The given system has equations:
![2x - 6y = 8....(1)](https://tex.z-dn.net/?f=2x%20-%206y%20%3D%208....%281%29)
![5x- 4y = 31....(2)](https://tex.z-dn.net/?f=5x-%204y%20%3D%2031....%282%29)
We make x the subject in the first equation to get:
![x = 4 + 3y...(3)](https://tex.z-dn.net/?f=x%20%3D%204%20%20%2B%203y...%283%29)
Put equation 3 into equation 2 to get:
![5(4 + 3y) - 4y = 31](https://tex.z-dn.net/?f=5%284%20%2B%203y%29%20-%204y%20%3D%2031)
Expand:
![20 + 15y - 4y = 31](https://tex.z-dn.net/?f=20%20%2B%2015y%20-%204y%20%3D%2031)
![15y - 4y = 31 - 20](https://tex.z-dn.net/?f=15y%20-%204y%20%3D%2031%20-%2020)
![11y = 11](https://tex.z-dn.net/?f=11y%20%3D%2011)
![y = 1](https://tex.z-dn.net/?f=y%20%3D%201)
Put y=1 into equation 3 and solve for x.
![x = 4 + 3( 1) = 7](https://tex.z-dn.net/?f=x%20%3D%204%20%2B%203%28%201%29%20%3D%207)
The correct ordered pair is (7,1)