Solve the system of equations. If there is no solution to the system, give a reason.
-$$\begin{array} { c }
x - 6 y = 4 \
6 x - 5 y = 24
\end{array}$$
A) No solution; Inconsistent system of equations
B) $( 5,4 )$
C) $( 4,0 )$
D) $( - 4 , - 1 )$

Question

Solve the system of equations. If there is no solution to the system, give a reason.
-$$\begin{array} { c } 
x - 6 y = 4 \
6 x - 5 y = 24
\end{array}$$
A) No solution; Inconsistent system of equations
B) $( 5,4 )$
C) $( 4,0 )$
D) $( - 4 , - 1 )$

Quizplus · Accepted Answer

To solve the system of equations, we can use either substitution or elimination method. Here, using elimination seems straightforward. Multiply the first equation by 6 to align the x coefficients:$$6(x - 6y) = 6(4)$$$$6x - 36y = 24$$Now, we have:$$6x - 36y = 24$$$$6x - 5y = 24$$Subtracting the second equation from the modified first equation eliminates $x$, but this step is unnecessary because we can see that the original equations are not multiples of each other, indicating they are not parallel and thus have a solution. Instead, we can solve the system directly.From the first equation:$$x = 6y + 4$$Substitute $x$ in the second equation:$$6(6y + 4) - 5y = 24$$$$36y + 24 - 5y = 24$$$$31y = 0$$$$y = 0$$Substitute $y = 0$ back into the first equation:$$x - 6(0) = 4$$$$x = 4$$Thus, the solution is $(4, 0)$.

Solve the System of Equations x−6y=46x−5y=24\begin{array} { c } x - 6 y = 4 \\6 x - 5 y = 24\end{array}x−6y=46x−5y=24​

Solve the System of Equations $\begin{array} { c } x - 6 y = 4 \\6 x - 5 y = 24\end{array}$