Q8. - Algebra 1

Question

What is the solution of the following system of equations?

$\mathbf{ }\{\begin{array}{l}y=6x-1\\ y=6x+4\end{array}$

$\mathit{F}$ $\mathbf{(}\mathbf{2}\mathbf{,}\mathbf{11}\mathbf{)}$

$\mathit{G}$ $\mathbf{(}\mathbf{-}\mathbf{3}\mathbf{,}\mathbf{-}\mathbf{14}\mathbf{)}$

$\mathit{H}$ $\mathbf{(}\mathbf{7}\mathbf{,}\mathbf{5}\mathbf{)}$

$\mathit{J}$ No solution

Step-by-Step Solution

Answer

There is no solution of the given system of equations. Therefore, the option $\mathit{J}$ is correct.

Step 1. Write the given system of equations.

The given system of equations is:

$\begin{array}{l}y=6x-1\text{ ...}\left(1\right)\\ y=6x+4\text{ ...}\left(2\right)\end{array}$

Step 2. Solve the given system of equations.

Substitute the value of $y$ from the equation (1) in the equation (2).

$\begin{array}{c}y=6x+4\\ 6x-1=6x+4\\ 6x-6x=4+1\\ 0=5\end{array}$

The condition obtained is $0=5$ which is false. Therefore, the given system of equations has no solution.

Therefore, there is no solution of the given system of equations. Therefore, the option $J$ is correct.