A student is trying to solve the set of two equations given below:

Equation A: x + z = 6
Equation B: 2x + 4z = 1

Which of the following is a possible step used in eliminating the z-term?

Multiply equation B by 4.

Multiply equation A by 2.***

Multiply equation A by −4.***

Multiply equation B by 2.

(either b or c)

b would be used to eliminate x

but
you are supposed to eliminate z
so
c
which would give you -4z+4z = 0

The correct possible step used in eliminating the z-term is to multiply equation A by −4.

To eliminate the z-term in the given set of equations, you need to perform some operations on the equations so that when you add or subtract them, the z-term cancels out.

In this case, you want to eliminate the z-term. Looking at the possible steps given, you can determine if multiplying equation A by 2 or multiplying equation A by -4 would achieve this.

If you multiply equation A by 2, the resulting equation would be:

2(x + z) = 2(6)
2x + 2z = 12

Notice that the z-term is still present, so multiplying equation A by 2 does not eliminate the z-term.

If you multiply equation A by -4, the resulting equation would be:

-4(x + z) = -4(6)
-4x - 4z = -24

Here, the z-term has been affected by the multiplication, and it has become -4z. In this case, the negative sign is important because we are trying to eliminate the z-term. So multiplying equation A by -4 does eliminate the z-term.

Therefore, the correct answer is c) Multiply equation A by -4.