Determine if $\left( 4 , - \frac { 1 } { 3 } \right)$ is a solution of the system $\left\{ \begin{array} { l }
5 x - 3 y = 21 \
\frac { 1 } { 2 } x - 3 y = 3
\end{array} \right.$
A) not a solution
B) solution

Question

Determine if $\left( 4 , - \frac { 1 } { 3 } \right)$ is a solution of the system $\left\{ \begin{array} { l } 
5 x - 3 y = 21 \
\frac { 1 } { 2 } x - 3 y = 3
\end{array} \right.$
A) not a solution
B) solution

Quizplus · Accepted Answer

To determine if $(4, -\frac{1}{3})$ is a solution, substitute $x = 4$ and $y = -\frac{1}{3}$ into both equations. For the first equation, $5(4) - 3(-\frac{1}{3}) = 20 + 1 = 21$, which matches the right side. For the second equation, $\frac{1}{2}(4) - 3(-\frac{1}{3}) = 2 + 1 = 3$, which also matches the right side. Since the pair satisfies both equations, it is a solution.

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