Answered

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.

Verified Answer :

Neuron

If
you would like to eliminate the z-term, you can do this using the following steps:


x + z = 6
/(-4)
2x + 4z =
1

_____________

-4x -4z =
-24
2x + 4z = 1

_____________

-4x

  • 2x = -24 + 1

-2x = -23

x = 23/2


The
correct result would be x +
z = 6       /(-4); multiply equation A by -4.

Lanuel

A possible step which can be used in eliminating the z-term is: C. multiply equation A by -4.

Given the following data:

  • x + z = 6    ........equation A.
  • 2x + 4z = 1   ......equation B.

What is a set of equations?

A set of equations is also referred to as a system of equations and it can be defined an algebraic equation that has only two (2) variables, which can be solved simultaneously.

In order to eliminate the z-term, we would subtract the second equation from 4 times the first equation:

Multiplying the first equation by 4, we have:

4[x + z = 6] = 4x + 4z = 24

Subtracting the two equations, we have:

[4x + 4z - 24 - 2x - 4z - (-1)] = 0

2x - 23 = 0

2x = 23

x = 23/2

x = 11.5.

In conclusion, a possible step which can be used in eliminating the z-term is to multiply equation A by -4.

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