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:
\(x+3y=5 (1)\\x-3y=-1 (2)\\________\\\)
\(2x=4 (3)\)
We can find x with the equation (3)
\(x=\frac{4}{2}\\x=2\)
Now we can replace x=2 in the equation (1) to find y
\(x+3y=5 (1)\\2+3y=5\\3y=5-2\\3y=3\\y=\frac{3}{3}\\y=1\)
Now, we have found x and y
x=2
y=1
The second way is clearing x from equation 1
\(x+3y=5\\x=5-3y (4)\)
Now, we can replace \(x=5-3y\) in the equation (2)
\(x-3y=-1 (2)\\(5-3y)-3y=-1\\5-6y=-1\\-6y=-6\\y=\frac{-6}{-6} \\y=1\)
Now, we can replace y=1 in the equation (1), (2) or (4) to find x
We will use the equation (1)
\(x+3y=5\\x+3(1)=5\\x+3=5\\x=5-3\\x=2\)
We have verified that by the two forms x = 2 and y = 1
