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how to solve a 4 variable equations

0 votes
4w+x+2y-3z=-16

-3w+3x-y+4z=20

5w+4x+3y-z=-10

-w+2x+5y+z=-4
asked Mar 10, 2014 in ALGEBRA 2 by futai Scholar

2 Answers

0 votes

Elimination method :

The system of equations are

image   → ( 1 )

image    → ( 2 )

image   → ( 3 )

image     → ( 4 )

To get the eq'ns (1) & (2) that contain opposite terms multiply the eq (2) by 2.

Write the equations in column form and add the equations to eliminate y - variable.

image

The resultant equation is  image  → ( 4 )

To get the eq'ns (2) & (3) that contain opposite terms multiply the eq (2) by 3.

Write the equations in column form and add the equations to eliminate y - variable.

image

The resultant equation is  image  → ( 5 )

To get the eq'ns (3) & (4) that contain opposite terms multiply the eq (3) by 5 and eq (4) by 3.

Write the equations in column form and Subtract the equations to eliminate y - variable.

image

The resultant equation is  image  → ( 6 )

answered Apr 15, 2014 by lilly Expert
0 votes

To get the eq'ns (4) & (5) that contain opposite terms multiply the eq (4) by 2.

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

image

The resultant equation is  image  → ( 7 )

To get the eq'ns (4) & (6) that contain opposite terms multiply the eq (4) by 7.

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

image

The resultant equation is  image  → ( 8 )

To get the eq'ns (7) & (8) that contain opposite terms multiply the eq (8) by 31.

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

image

The resultant equation is  image.

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

image.

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

image.

Substitute the values of image , image, and imagein eq (1), and solve for y.

image.

Therefore, solution of the given system is imageimage, image, and image.

answered Apr 15, 2014 by lilly Expert

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