Solve the system of equations. 3x+4y+4z=4, 5x+7y+3z=5 and 4x+5y+7z=7

We'll label the equations to keep track of what we're doing3x+4y+4z=4    A5x+7y+3z=5    B4x+5y+7z=7     CNormally in Gaussian elimination we'd pick put a constant on each equation and combine to cancel out a variable in all but one.  But here we have an opportunity to make the coefficient 1 on our variables in at least one equation.  This is a pretty good thing to do when solving these by hand.x + y + 3z = 3         D=C-A-2x - 3y + z = -1     E=A-BLet's eliminate x from two equations-y + 7z = 5          F=2D+E-y + 5z = 5         G=4D-CLet's eliminate y2z = 0               H=F-Gz = 0-y + 7z = 5y = -5x + y + 3z  = 3x - 5 + 0  = 3x = 8Answer: (x,y,z)=(8,-5,0)Check:3(8)+4(-5)+4(0) = 4, good5(8)+7(-5)+3(0)=5, good4(8)+5(-5)+7(0)=7, good