Question

A system of two equations is shown below:

Equation C: a = 3b + 6
Equation D: a = 7b − 1

What value of a can be substituted into equation D to solve the system of equations?
3b
7b
3b + 6
7b − 1

Answer 1

The answer would be 3b + 6 because as you can see a = 3b + 6 and a = 7b - 1 so the two equations are equal to each other since they both are equal to a.

Answer 2

Answer: The correct option is (C) a = 3b + 6.

Explanation: The give system of two linear equations is as follows :

`\textup{Equation C}:a=3b+6~~~~~~~~~~~~~~~~~~~~~~(i)\\\\\textup{Equation D}:a=7b-1~~~~~~~~~~~~~~~~~~~~~~(ii)`

We are to select the correct value of a that can be substituted into equation D to solve the given system.

Since we need to solve the given system, so we should either substitute the value of a from equation C into equation D or from equation D into equation C.

If we substitute value of a from equation D into equation D, then we arrive at

`a=7b-1\\\\\Rightarrow 7b-1=7b-1\\\\\Rightarrow 0=0.`

This does not give us any result.

On the other hand, if we substitute the value of a from C into D, then we arrive at

`a=7b-1\\\\\Rightarrow 3b+6=7b-1\\\\\Rightarrow -4b=-7\\\\\Rightarrow  b=-(7)/(4).`

Thus, we should substitute a = 3b + 6 into equation D.

Option (C) is correct.