Determine whether each ordered pair is a solution of the...

Determine whether each ordered pair is a solution of the system of equations.
$$\left\{\begin{array}{l}
4 x^{2}+y=3 \\
-x-y=11
\end{array}\right.$$
(a) (2,-13)
(b) (-2,-9)
(c) $\left(-\frac{3}{2}, 6\right)$
(d) $\left(-\frac{7}{4},-\frac{37}{4}\right)$

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Key Concepts

System of Equations

A system of equations consists of two or more equations that are solved together because they share common variables. In this context, the ordered pair must satisfy each equation simultaneously to be a solution, making the understanding of how multiple equations interact critical.

Solution Verification

Checking if an ordered pair is a solution involves substituting the values into each equation to see if both equations hold true. This method ensures that the candidate solution adheres to all conditions imposed by the system.

Substitution Method

The substitution method is a technique where the variables are replaced with specific values (from a candidate solution) in each equation. This process helps verify if the equations evaluate correctly, confirming or rejecting the ordered pair as a valid solution.

Quadratic Equations

One of the equations in the system involves a quadratic term. Understanding quadratic equations is important here because substituting the x-value into the quadratic expression requires careful computation to ensure the correct evaluation when checking for solutions.

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