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