C30† Find all solutions to the linear system:
x + y = 5
2x − y = 3
To solve this system of equations, we will first multiply equation 1 by -2 and add to equation 2:
x + y = 5
- 3y = -7
Now we can divide equation 2 by -3 to solve for y:
x + y = 5 y = 7/3
Lastly, we will plug our value for y into equation 1 to solve for x:
x + (7/3) = 15/3 x = 8/3
Our final solution is: x = 8/3, y = 7/3