Question

a system of equations is shown below: equation a: 2c = d − 8 equation b: c = 3d 8 which of the following steps should be performed to eliminate variable d first? multiply equation b by 2. multiply equation a by 2. multiply equation b by 3. multiply equation a by −3.

Answer 1

If you would like to know which of the following steps should be performed to eliminate variable d first, you can find this using the following steps:

equation a: 2c = d - 8      /*(-3)
equation b: c = 3d + 8
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-6c = -3d + 24
c = 3d + 8
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-6c + c = -3d + 24 + 3d + 8
-5c = 32
5c = -32
c = -32/5

The correct result would be: multiply equation a by −3.

Answer 2

The step that could eliminate the variable d is: (d) multiply equation a by -3

How to eliminate the variable d?

The equations are given as:

2c = d − 8

c = 3d + 8

Multiply the first equation by -3

-6c = -3d + 24

Add this to the second equation

c - 6c = 3d - 3d + 8 + 24

This gives

-5c = 32

Variable d has been eliminated.

Hence, the step that could eliminate the variable d is: (d) multiply equation a by -3

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