In Exercises 1–4, determine whether the given ordered pair is a solution of the system. (- 3, 5) 9x + 7y = 8 8x - 9y = - 69

Verified step by step guidance

1. Step 1: Identify the ordered pair given, which is (-3, 5). Here, x = -3 and y = 5.
2. Step 2: Substitute x = -3 and y = 5 into the first equation: $\mathrm{9x\; +\; 7y\; =\; 8}$. This becomes $9(-3)\; +\; 7(5)$.
3. Step 3: Simplify the left side of the first equation after substitution: calculate $9(-3)\; +\; 7(5)$ to check if it equals 8.
4. Step 4: Substitute x = -3 and y = 5 into the second equation: $8x\; -\; 9y\; =\; -69$. This becomes $8(-3)\; -\; 9(5)$.
5. Step 5: Simplify the left side of the second equation after substitution: calculate $8(-3)\; -\; 9(5)$ to check if it equals -69. If both equations are true with these values, 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 these 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, which confirms whether the pair satisfies the system.

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. This process is crucial to determine if the ordered pair solves the system.