solve the system of linear equations

Question

-x-y+3=-1

-x+y-3=3

x-y-z=5

Answer 1

Elimination method

Given equations are -x-y+3 = -1

Subtract 3 from each side.

-x-y+3-3 = -1-3

-x-y = -4 -----> (1)

-x+y-3 = 3

Add 3 to each side.

-x+y = 6 ----> (2)

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

To eliminate the y variable, add equations (1)&(2).

-x-y = -4

-x+y = 6

__________

-2x = 2

Divide to each side by negitive 2.

x = -1

To elimnate x,y variable,add the equations (2)&(3).

-x+y = 6

x-y-z = 5

__________

-z = 11

Multiple to each side by negitive one.

z = -11

Substitute the values x,z in equation (3).

-1-y+11 = 5

-y+10 = 5

-y = 5-10

-y = -5

y = 5

Solution x = -1, y = 5, z = -11.