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Find the complete solution of the linear system, or show that it is inconsistent. (If the system has infinitely many solutions, express your answer in terms of t, where x = x(t), y = y(t), and z = t. If there is no solution, enter NO SOLUTION.) x ? 2y + z = 3 2x ? 5y + 6z = 7 2x ? 3y ? 2z = 5 (x, y, z) =

Respuesta :

The solution of a linear equation is (-2,5,4).

The equations given in the questions are,

x - y + 2z = 1 ..[1]

3x + y + 5z = 19  ..[2]

2x - y - 2z = -17 ...[3]

Putting the value of y from [1] in [2]and [3]

y = x+ 2z -1

3x + (x+ 2z -1) + 5z = 19  

4x + 7z = 20  ...[4]

2x - (x+ 2z -1) - 2z = -17

x - 4z = -18   ...[5]

Solving equations [4] and [5] by substitution:

Putting values of x from [5] in [4]

x = 4z -14

4(4z -18) + 7z = 20

16z - 72+ 7z =20

23z = 92

z = 4

x = 4 × (92 ÷ 23) - 18

x = -2

y = (-2) + 2 × (92 ÷ 23) - 1

y = 5

(x,y,z) = (5.-2,4)

The solution of the equation is (-2,5,4).

Learn more about linear equations at

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