Giải hệ phương trình 2x - y = 1 x + y = 1

To solve the system of equations, we can use the method of addition or substitution. Let's use the method of addition. We have the system of equations: \[ \begin{cases} 2x - y = 1 \\ x + y = 1 \end{cases} \] First, let's add the two equations together to eliminate the variable \(y\): \[ (2x - y) + (x + y) = 1 + 1 \] \[ 3x = 2 \] Now, solve for \(x\): \[ x = \frac{2}{3} = 0.6666666666666666 \] Next, substitute the value of \(x\) into one of the original equations to solve for \(y\). Let's use the second equation: \[ x + y = 1 \] \[ \frac{2}{3} + y = 1 \] Solve for \(y\): \[ y = 1 - \frac{2}{3} = \frac{1}{3} = 0.3333333333333333 \] So, the solution to the system of equations is \( x = 0.6666666666666666 \) and \( y = 0.3333333333333333 \).