Solve the system in terms of the arbitrary variable x 6x 4y

Solve the system in terms of the arbitrary variable x. 6x - 4y + z = 7 x + y = 13 The solution set is {(, , )}. (Type an expression using x as the variable.)

Solution

We have 6x-4y+z = 7 or, -4y+z = 7-6x …(1) and x +y = 13 or, y = 13-x…(2)

Since y = 13-x, on substituting this value of y in the 1^st equation we get -4(13-x) +z = 7-6x or, -52 +4x +z = 7-6x or, z = 7-6x +52-4x or, z = 59-10x.

Then the solution set is (x,y,z) = (x , 13-x, 59-10x)