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In some cases, neither of the two equations in the system will contain a variable with a coefficient of 1, so we must take a further step to isolate it. Let's say we now have3C+4D=52C+5D=2None of these terms has a coefficient of 1. Instead, we'll pick the variable with the smallest coefficient and isolate it. Move the term with the lowest coefficient so that it's alone on one side of its equation, then divide by the coefficient. Which of the following expressions would result from that process?a. C=53−43Db. C=1−52Dc. D=25−25Cd. D=54−34C

Respuesta :

Answer:

According to the instructions given, only options a and b are correct.

That is,

C = (5/3) - (4D/3)

C = 1 – (5D/2)

D= -4/7

C= 17/7

Explanation:

3C + 4D = 5 and 2C + 5D = 2

So, following the instructions from the question,

1) we'll pick the variable with the smallest coefficient and isolate it.

In eqn 1, C has the smallest coefficient,

3C = 5 - 4D (isolated!)

In eqn 2, C still has the smallest coefficient,

2C = 2 - 5D

2) Move the term with the lowest coefficient so that it's alone on one side of its equation, then divide by the coefficient.

For eqn 1,

3C = 5 - 4D, divide through by the coefficient of C,

C = (5/3) - (4D/3)

This matches option a perfectly.

For eqn 2,

2C = 2 - 5D, divide through by the coefficient of C,

C = (2/2) - (5D/2) = 1 - (5D/2)

This matches option b perfectly!

Further solving the equations now,

Since C = C

(5/3) - (4D/3) = 1 - (5D/2)

(5D/2) - (4D/3) = 1 - (5/3)

(15D - 8D)/6 = -2/3

7D/6 = -2/3

D = -4/7

Substituting this into one of the eqns for C

C = 1 - (5D/2)

C = 1 - (5/2)(-4/7) = 1 - (-10/7) = 1 + (10/7) = 17/7.

QED!

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