Question

Solve the linear equation in three variables : x-2y +3z=7, 2x +y+z =4,-3x+2y-z =-10

Answer 1

Answer:

x-2y+3z=7 .............equation 1

2x+y+z=4 ..............equation 2

-3x+2y-z=-10 ..........equation 3

solve equation 2&3

equation 2 = 2x+y +z=4

equation 3 = -3x+2y-z=-10

= -x+3y =6 ......equation 4

solve equation 1&2

equation 1 = x-2y+3z = 7

equation 2×3 = 6x+3y+3z =12

( changing the signs) - - - -

= -5x-5y = -5 ( ÷ by -)

= 5x+5y = 5........equation

solve equation 4&5

equation 4×5 = -5x +15y = 30

equation 5. = 5x +5y =5

= 20y = 35

y = 35/20

y =7/4

substitute y=7/4 in equation 4

-x +3y = 6

-x +3(7/4) = 6

-6 +21/4=x

-24+21 = x

4

-3/4 =x

substitute x= -3/4 & y= 7/4 in equation 2

2x + y +z =4

2(-3/4)+7/4+z= 4

-6/4 + 7/4 = 4

-6+7 + z= 4

4

1 + z = 16

z = 16 -1

z = 15

therefore x=-3/4, y=7/4,z=15