X+y=5 3x+y=7

You have a system of two linear equations with two variables:

1. \(x + y = 5\)
2. \(3x + y = 7\)

To solve for \(x\) and \(y\), we can use either substitution or elimination methods. Here, we can easily use the elimination method by subtracting the first equation from the second to eliminate \(y\):

Subtract equation 1 from equation 2:

\(3x + y - (x + y) = 7 - 5\) Which simplifies to: \(3x + y - x - y = 7 - 5\) \(2x = 2\)

Now, solve for \(x\): \(x = \frac{2}{2} = 1\)

Now that we have \(x\), we plug it back into either of the original equations to solve for \(y\). Let's use the first equation:

\(x + y = 5\) \(1 + y = 5\) Solve for \(y\): \(y = 5 - 1\) \(y = 4\)

So, the solution to the system of equations is \(x=1\) and \(y=4\).