Solve the system of linear equations x 2y 4z 26 3x 4y 7

Solve the system of linear equations. x + 2y + 4z = 26 -3x - 4y + 7z = 34 If there are an infinite number of solutions, enter IS in each answer field. If there are no so answer field. x = y = z =

Solution

x +2y + 4z = 26

-3x -4y +7z = 34

there would be infinite solution as there are 3 variables and two equations

Let z be free variable and z =t

So, x +2y +4t =26

-3x -4y +7t = 34

multiply equ 1 by 3:

3x +6y +12t = 78

-3x -4y +7t = 34

----------------------- (add)

2y = 112 - 19t

y = 56 -19t/2

x = 26 - 4t - (112 -19t)

= 15t - 86

z =t