Question

PLESE HELP .A student is trying to solve the set of two equations given below: Equation A: x + z = 6 Equation B: 2x + 3z = 1 Which of the following is a possible step used in eliminating the z-term?

Multiply equation B by 3.
Multiply equation A by 2.
Multiply equation B by 2.
Multiply equation A by −3.

Answer 1

D. Multiply equation A by −3.

Explanation:

We have been given a system of equations.

Equation A:
`x + z = 6`

Equation B:
`2x + 3z = 1`

We are asked to determine the possible step used in eliminating the z-term.

We can see that coefficient of z term is equation B is 3, so eliminate z term from the both equations the coefficient of z term is equation A should be
`-3`.

We can make coefficient of z term to
`-3` in equation A by multiplying equation A by
`-3` that will give us:

`-3\cdot x + -3\cdot z =-3\cdot 6`

`-3x-3z =-18`

Now, adding equation A and equation B the z term will get eliminated.

Therefore, option D is the correct choice.

Answer 2

You need to choose which term you'd like to eliminate first.

If you want to eliminate the term 'x' then you need to have the constant of both 'x' term the same. Equation A has 'x' with constant '1'. Equation B has '2x' with constant '2'. To eliminate 'x', we need to multiply equation A by '2' to get 2x + 2z = 12, then we can SUBTRACT Equation B from A

To eliminate term 'z', we multiply equation A by 3 to get 3x + 3z = 18 then we can SUBTRACT Equation B from A

Answer: Option B 'Multiply A by 2'