To show that the system is not consistent, we can use the method of elimination. We'll start by eliminating the variable z.
Multiplying the first equation by 3, we get 6x + 18y = -33.
Adding this equation to the second equation, we get:
(6x + 20y) + (6x + 18y) - 6z = -3 + (-33)
12x + 38y - 6z = -36.
But this equation is inconsistent with the third equation 6y - 18z = -1, as we cannot find values of x, y, and z that satisfy all three equations simultaneously. Therefore, the system of equations is not consistent.
Show that the system of equations 2x+6y=-11, 6x+20y-6z=-3, 6y-18z=-1 is not consistent.
1 answer
1 answer