Question

Tell whether the ordered pair is a solution of the given system. (-2,-4) {y=1/2x -3, y=-2x-8}

Answer 1

Answer:

The ordered pair $(-2,\, -4)$ is indeed a solution to the system:

$\left\lbrace\begin{aligned} & y = \frac{1}{2}\, x - 3 \\ & y = -2\, x - 8\end{aligned}\right.$.

Step-by-step explanation:

Consider a system of equations about variables $x$ and $y$. An ordered pair $(x_{0},\, y_{0})$ (where $x_{0}$ and $y_{0}$ are constant) is a solution to that system if and only if all equations in that system hold after substituting in $x = x_{0}$ and $y = y_{0}$.

For the system in this question, $(-2,\, -4)$ would be a solution only if both equations in the system hold after replacing all $x$ in equations of the system with $(-2)$ and all $y$ with $(-4)$.

The $\texttt{LHS}$ of the equation $y = (1/2)\, x - 3$ would become $(-4)$. The $\texttt{RHS}$ of that equation would become $(1/2) \, (-2) - 3$. The two sides are indeed equal.

Similarly, the $\texttt{LHS}$ of the equation $y = -2\, x - 8$ would become $(-4)$. The $\texttt{RHS}$ of that equation would become $(-2)\, (-2) - 8$. The two sides are indeed equal.

Thus, $x = (-2)$ and $y = (-4)$ simultaneously satisfy both equations of the given system. Therefore, the ordered pair $(-2,\, -4)$ would indeed be a solution to that system.