# SOLUTION: Solve the system for each variable: y+z=6 x+5y-4Z=4 x-3y+5z=7

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 Click here to see ALL problems on Linear-equations Question 54149: Solve the system for each variable: y+z=6 x+5y-4Z=4 x-3y+5z=7Answer by ankor@dixie-net.com(16524)   (Show Source): You can put this solution on YOUR website!y+z=6 x+5y-4Z=4 x-3y+5z=7 : Take the last two equations and eliminate x: x + 5y - 4z = 4 x - 3y + 5z = 7 ----------------subtract 0x +8y - 9z = -3 : Using the 1st equation for substitution for y in 8y - 9z = -3: y + z = 6 y = (6-z) : 8(6-z) - 9z = -3 48 - 8z - 9z = - 3 -17z = -3 -48 -17z = -51 z = -51/-17 z = +3 : : Find y using the 1st equation, substituting 3 for z y + z = 6 y + 3 = 6 y = 6 - 3 y = + 3 also : Find x using the 2nd equation, substituting 3 for y and z x + 5y - 4z = 4 x +5(3) - 4(3) = 4 x + 15 - 12 = 4 x + 3 = 4 x = 4 - 3 x = +1 : Check all three solutions in the 3rd equation: x - 3y + 5z = 7 1 - 3(3) + 5(3) = 1 - 9 + 15 = 7; seems to be correct : Make sense to you??