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2/3x - 1/4y + 5/8z = 0, 1/5x + 2/3y - 1/4z = -7 and -3/5x + 4/3y - 7/8z = -5

0 votes

2/3x - 1/4y + 5/8z = 0, 1/5x + 2/3y - 1/4z = -7, -3/5x + 4/3y - 7/8z = -5

solve for x,y,z.

 

asked Feb 20, 2014 in ALGEBRA 2 by andrew Scholar

2 Answers

0 votes

Elimination method :

The system of equations are

image         → ( 1 )

image      → ( 2 )

image  → ( 3 )

Change the equations from fraction form to linear equation.

The L.C.M of 3,4, and 8 in eq (1) is 24, so multiply eq (1) by 24.

image                    → ( 4 )

The L.C.M of 5,3, and 4 in eq (2) is 60, so multiply eq (2) by 60.

image         → ( 5 )

The L.C.M of 5,3, and 8 in eq (3) is 120, so multiply eq (3) by 120.

image( 6 )

Write the eqn's (4) & (5) in column form and add the equations to eliminate z - variable.

image

The resultant equation is image ( 7 )

To get the eq'ns (5) & (6) that contain opposite terms multiply the eq (5) by 7.

Write the equations in column form and subtract the equations to eliminate z - variable.

image

The resultant equation is image ( 8 )

answered Apr 10, 2014 by lilly Expert
0 votes

To get the eq'ns (7) & (8) that contain opposite terms multiply the eq (7) by 13 and eq (8) by 14.

Write the equations in column form and subtract the equations to eliminate x - variable.

image

The resultant equation is image.

Substitute the value of image in eq (7), and solve for x.

image

Substitute the values of image and image in eq (4), and solve for z.

image

image.

Therefore, solution of the given system is image

answered Apr 10, 2014 by lilly Expert

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