Question

Solve the following system using the elimination method. Enter your answer as an ordered pair in the form (x,y) if there is one, unique solution. Enter all if there are infinitely many solutions and enter none if there are no solutions. 7x - 6y = 2 - 14x + 12y = 6

Answer 1

Given the system of equations

`\begin{cases}7x-6y=2 \\ -14x+12y=6\end{cases}`

Multiply the first equation by 2 and add it to the second equation, as shown below

`\begin{gathered} 2(7x-6y)=2(2) \\ \Rightarrow14x-12y=4 \end{gathered}`

Thus,

`\begin{gathered} \Rightarrow(-14x+12y)+(14x-12y)=6+4 \\ \Rightarrow0=10!!! \end{gathered}`

It is impossible that 0=10; thus, the system of equations does not have solutions, both lines are parallel