SOLUTION: solve the system of equations 5/4x - 4/3y + 5/4z = 7 5/16x + 3/4y - 3/16z = -7 3/4x -y + 3/4z = 6 x = __ , y = ___, and z = ___

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Question 267955: solve the system of equations
5/4x - 4/3y + 5/4z = 7
5/16x + 3/4y - 3/16z = -7
3/4x -y + 3/4z = 6
x = __ , y = ___, and z = ___
Answer by persian52(161)   (Show Source): You can put this solution on YOUR website!
(5)/(4)*x-(4)/(3)*y+(5)/(4)*z=7
►Multiply (5)/(4) by x to get (5x)/(4).
(5x)/(4)-(4)/(3)*y+(5)/(4)*z=7
►Multiply -(4)/(3) by y to get -(4y)/(3).
(5x)/(4)-(4y)/(3)+(5)/(4)*z=7
►Multiply (5)/(4) by z to get (5z)/(4).
(5x)/(4)-(4y)/(3)+(5z)/(4)=7
►Move all terms not containing x to the right-hand side of the equation.
(5x)/(4)=(4y)/(3)-(5z)/(4)+7
►Multiply each term in the equation by 4.
(5x)/(4)*4=(4y)/(3)*4-(5z)/(4)*4+7*4
►Simplify the left-hand side of the equation by canceling the common terms.
5x=(4y)/(3)*4-(5z)/(4)*4+7*4
►Simplify the right-hand side of the equation by simplifying each term.
5x=(16y)/(3)-5z+28
►Divide each term in the equation by 5.
(5x)/(5)=(16y)/(3)*(1)/(5)-(5z)/(5)+(28)/(5)
►Simplify the left-hand side of the equation by canceling the common terms.
x=(16y)/(3)*(1)/(5)-(5z)/(5)+(28)/(5)
►Simplify the right-hand side of the equation by simplifying each term.
=► x=(16y)/(15)-z+(28)/(5)
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(5)/(16)*x+(3)/(4)*y-(3)/(16)*z=-7
►Multiply (5)/(16) by x to get (5x)/(16).
(5x)/(16)+(3)/(4)*y-(3)/(16)*z=-7
►Multiply (3)/(4) by y to get (3y)/(4).
(5x)/(16)+(3y)/(4)-(3)/(16)*z=-7
►Multiply -(3)/(16) by z to get -(3z)/(16).
(5x)/(16)+(3y)/(4)-(3z)/(16)=-7
►Move all terms not containing y to the right-hand side of the equation.
(3y)/(4)=-(5x)/(16)+(3z)/(16)-7
►Multiply each term in the equation by 4.
(3y)/(4)*4=-(5x)/(16)*4+(3z)/(16)*4-7*4
►Simplify the left-hand side of the equation by canceling the common terms.
3y=-(5x)/(16)*4+(3z)/(16)*4-7*4
►Simplify the right-hand side of the equation by simplifying each term.
3y=-(5x)/(4)+(3z)/(4)-28
►Divide each term in the equation by 3.
(3y)/(3)=-(5x)/(4)*(1)/(3)+(3z)/(4)*(1)/(3)-(28)/(3)
►Simplify the left-hand side of the equation by canceling the common terms.
y=-(5x)/(4)*(1)/(3)+(3z)/(4)*(1)/(3)-(28)/(3)
►Simplify the right-hand side of the equation by simplifying each term.
=► y=-(5x)/(12)+(z)/(4)-(28)/(3)
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(3)/(4)*x-y+(3)/(4)*z=6
►Multiply (3)/(4) by x to get (3x)/(4).
(3x)/(4)-y+(3)/(4)*z=6
►Multiply (3)/(4) by z to get (3z)/(4).
(3x)/(4)-y+(3z)/(4)=6
►Move all terms not containing z to the right-hand side of the equation.
(3z)/(4)=-(3x)/(4)+y+6
►Multiply each term in the equation by 4.
(3z)/(4)*4=-(3x)/(4)*4+y*4+6*4
►Simplify the left-hand side of the equation by canceling the common terms.
3z=-(3x)/(4)*4+y*4+6*4
►Simplify the right-hand side of the equation by simplifying each term.
3z=-3x+4y+24
►Divide each term in the equation by 3.
(3z)/(3)=-(3x)/(3)+(4y)/(3)+(24)/(3)
►Simplify the left-hand side of the equation by canceling the common terms.
z=-(3x)/(3)+(4y)/(3)+(24)/(3)
►Simplify the right-hand side of the equation by simplifying each term.
=► z=-x+(4y)/(3)+8
_______________________________________________________________________________
x =(16y)/(15)-z+(28)/(5), y =-(5x)/(12)+(z)/(4)-(28)/(3), and z =-x+(4y)/(3)+8
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