{2х-3у=1 {3х+у=7

You have a system of linear equations to solve:

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

Let's solve this system step by step.

Step 1: Solve one of the equations for one variable

From Equation 2, we can express \(y\) in terms of \(x\):

\[ y = 7 - 3x \]

Step 2: Substitute into the other equation

Now, substitute \(y\) into Equation 1:

\[ 2x - 3(7 - 3x) = 1 \]

Step 3: Simplify and solve for \(x\)

Distributing the -3:

\[ 2x - 21 + 9x = 1 \]

Combine like terms:

\[ 11x - 21 = 1 \]

Add 21 to both sides:

\[ 11x = 22 \]

Now divide by 11:

\[ x = 2 \]

Step 4: Substitute back to find \(y\)

Now that we have \(x\), substitute it back into the expression for \(y\):

\[ y = 7 - 3(2) = 7 - 6 = 1 \]

Conclusion

The solution to the system of equations is:

\[ x = 2, \quad y = 1 \]

You can write the answer as the ordered pair:

\[ (x, y) = (2, 1) \]