Question

Select the correct answer choice and fill in the blanks

Answer 1

Given System of equations

`\begin{gathered} 42x\text{ - 7y }=\text{ 35} \\ -6x\text{ + y =}5 \end{gathered}`

Solving the equations simultaneously

From equation 2

`\begin{gathered} -6x\text{ + y = 5} \\ y\text{ = 5 + 6x} \end{gathered}`

Substituting the expression for y into equation 1:

`\begin{gathered} 42x\text{ - 7y = 35} \\ 42x\text{ - 7(5 + 6x) = 35} \end{gathered}`

Solving for x:

`\begin{gathered} 42x\text{ -35 - 42x = 35} \\ \text{Collect like terms} \\ 42x\text{ - 42x = 35 + 35} \\ 0\text{ = 70} \end{gathered}`

We can conclude that there is no solution to the system of equations and that the lines are parallel.

Answer:

The solution is the empty set (Option C)