Question

Equation A: x + z = 6 Equation B: 3x + 2z = 1 Which of the following is a possible step in eliminating the z-term?

a. Multiply equation A by -2.
b. Multiply equation B by 2.
c. Multiply equation A by 3.
d. Mulitply equation B by 3.

Answer 1

To eliminate a term, its coefficients in both equations must be opposite numbers.


`x+z=6 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |* (-2) \\ 3x+2z=1 \\ \\ -2x-2z=-12 \\ \underline{3x+2z=1 \ \ \ \ \ \ \ \ } \\ x=-11 \\ \\ x+z=6 \\ -11+z=6 \\ z=6+11 \\ z=17 \\ \\ (x,y)=(-11,17)`

The answer is A. multiply equation A by -2.