how do I solve: -3x-2y+4z=-15, 2x+5y-3z=3, 4x-y+7z = 15

Question

Solve systems of linear equations in three variables by the elimination method

-3x-2y+4z=-15

2x+5y-3z=3

4x-y+7z=15

Answer 1

-3x-2y+4z = -15 ---------> (1)

2x+5y-3z = 3 ----------> (2)

4x-y+7z = 15 ---------. (3)

multiple to each side of equation (2)by 2.

4x+10y-6z = 6 ----------> (4)

To eliminate the x value subtract equation (3) from (4).

4x+10y-6z = 6

4x-y+7z = 15

(-)  (+) (-)  (-)

___________

11y-13z = -9 ------------> (5)

multiple to each side of equation (2) by 3 and (1) by 2 and add the equations.

-6x-4y+8z = -30

6x+15y-9z = 9

____________

11y-z = -21 ---------> (6)

to eliminate the y value subtract the equation (6) from (5).

11y-13z =-9

11y-z = -21

(-) (+) (+)

__________

-12z = 12

Divide to each side by negitive 12.

-12z/-12 = 12/-12

z =- 1

Substitute the z value in (6)

11y+1 = -21

Subtract 1 from each side.

11y+1-1 = -21-1

11y = -22

Divide to each side by 11.

y/11 = -22/11

y = -2

Substitute the z,y values in (2).

2x+5*-2-3*-1 = 3

2x-10+3 = 3

2x -7 = 3

add 7 to each side.

2x -7+7 = 7+3

2x = 10

Divide to each side by 2.

2x/2 = 10/2

x = 5

Solution of given system is x = 5, y = -2, z = -1.