) -x_(1)-x_(2)-2x_(4)+2x_(5)=1 2x_(1)-x_(2)+x_(3)-2x_(4)+2x_(5)=-1 x_(1)-2x_(2)-x_(4)-x_(3)=0 2x_(1)

To solve the given system of linear equations, we can use the method of substitution or elimination. Let's solve it using the elimination method.The given system of equations is: Step 1: Add equation (1) and equation (4) to eliminate : Step 2: Multiply equation (3) by 2 and add it to equation (2) to eliminate : Step 3: Multiply equation (1) by 2 and add it to equation (6) to eliminate : Step 4: Substitute into equation (5) to find and : Step 5: Substitute into equation (6) to find and : Step 6: Substitute and into equation (8) to find : Therefore, the solution to the given system of equations is:\[\begin{align*}x_{1} &= \frac