Answer:
Given the system of equations, what is the solution?
x + 3y = 5
x - 3y = -1
The answer is {(2, 1)}
x=2 and y=1
Step-by-step explanation:
We can find the solution in two ways,the first way is by term elimination the equations:
![x+3y=5 (1)\\x-3y=-1 (2)\\________\\](https://tex.z-dn.net/?f=x%2B3y%3D5%20%281%29%5C%5Cx-3y%3D-1%20%282%29%5C%5C________%5C%5C)
![2x=4 (3)](https://tex.z-dn.net/?f=2x%3D4%20%283%29)
We can find x with the equation (3)
![x=\frac{4}{2}\\x=2](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B4%7D%7B2%7D%5C%5Cx%3D2)
Now we can replace x=2 in the equation (1) to find y
![x+3y=5 (1)\\2+3y=5\\3y=5-2\\3y=3\\y=\frac{3}{3}\\y=1](https://tex.z-dn.net/?f=x%2B3y%3D5%20%281%29%5C%5C2%2B3y%3D5%5C%5C3y%3D5-2%5C%5C3y%3D3%5C%5Cy%3D%5Cfrac%7B3%7D%7B3%7D%5C%5Cy%3D1)
Now, we have found x and y
x=2
y=1
The second way is clearing x from equation 1
![x+3y=5\\x=5-3y (4)](https://tex.z-dn.net/?f=x%2B3y%3D5%5C%5Cx%3D5-3y%20%284%29)
Now, we can replace
in the equation (2)
![x-3y=-1 (2)\\(5-3y)-3y=-1\\5-6y=-1\\-6y=-6\\y=\frac{-6}{-6} \\y=1](https://tex.z-dn.net/?f=x-3y%3D-1%20%282%29%5C%5C%285-3y%29-3y%3D-1%5C%5C5-6y%3D-1%5C%5C-6y%3D-6%5C%5Cy%3D%5Cfrac%7B-6%7D%7B-6%7D%20%5C%5Cy%3D1)
Now, we can replace y=1 in the equation (1), (2) or (4) to find x
We will use the equation (1)
![x+3y=5\\x+3(1)=5\\x+3=5\\x=5-3\\x=2](https://tex.z-dn.net/?f=x%2B3y%3D5%5C%5Cx%2B3%281%29%3D5%5C%5Cx%2B3%3D5%5C%5Cx%3D5-3%5C%5Cx%3D2)
We have verified that by the two forms x = 2 and y = 1