Solving simultaneous equations for motion

Question

Textbook asked student to solve the following simultaneous equations where x is distance in cm and t is time in minutes:

1. x = 2t
2. x = -4t -20

I multiplied equation 1 by the 't' coefficient of equation 2, -4, and vice-versa multiplied equation 2 by the 't' coefficient of 1, 2, to get:

1. -4x = -8t
2. 2x = -8t-40

I then took the second equation from the first to get:

-6x = -40 so solved x to be -40/-6 or 6.67.

Substituting this value of x into the original equation 1 gave t to be 3.33.

However, the textbook answer was x= -6.67 and t= -3.33.

Where did I go wrong?

Answer 1

When you "take the second equation from the first", you should end up with $6x=-40$, not $-6x=-40$.