Determine whether the given ordered pair is a solution of the system. $(-3,5)$
$\(\begin{cases}\)9x + 7y = 8 \\8x - 9y = -69\(\end{cases}\)$

Verified step by step guidance

1. Identify the ordered pair given: \((-3, 5)\), where \(x = -3\) and \(y = 5\).
2. Substitute \(x = -3\) and \(y = 5\) into the first equation \$9x + 7y = 8$ to check if the equation holds true.
3. Calculate the left side of the first equation: \$9(-3) + 7(5)$ and compare it to the right side, which is \(8\).
4. Substitute \(x = -3\) and \(y = 5\) into the second equation \$8x - 9y = -69$ to check if this equation is also satisfied.
5. Calculate the left side of the second equation: \$8(-3) - 9(5)\( and compare it to the right side, which is \)-69$. If both equations are true, then the ordered pair is a solution to the system.

Key Concepts

Systems of Linear Equations

A system of linear equations consists of two or more linear equations with the same variables. The solution to the system is the set of values that satisfy all equations simultaneously. Understanding how to work with systems is essential for determining if a given ordered pair is a solution.

Ordered Pair as a Solution

An ordered pair (x, y) is a solution to a system if substituting x and y into each equation makes both equations true. This involves replacing variables with the given values and verifying the equality holds for each equation.

Substitution and Verification

Substitution involves plugging the values of x and y from the ordered pair into each equation. Verification means checking if the resulting expressions on both sides of the equation are equal, confirming whether the ordered pair satisfies the system.