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An ordered pair is used to represent two related numbers within a coordinate system, such as \((-2, 5)\). The first number is always the x-coordinate (horizontal position), and the second number is the y-coordinate (vertical position). Ordered pairs are essential in solving equations because they show specific points on a coordinate plane.

For example, in the pair \((-2, 5)\), the value -2 indicates the position on the x-axis, and 5 indicates the position on the y-axis. This means that if you move 2 units to the left of the origin (0,0), and then 5 units up, you will find the point represented by \((-2, 5)\).

By checking if these coordinates satisfy a given equation, you can determine if they are solutions to the equation.

Solving equations is the process of finding the values of variables that make a mathematical statement true. Here is a general approach to solving equations:

• Identify the equation you need to solve.
• Isolate the variable on one side of the equation by performing arithmetic operations like addition, subtraction, multiplication, or division.

In our exercise, we need to verify if \((-2, 5)\) satisfies the equation \(2x - y = -9\). This involves substituting the ordered pair into the equation and simplifying it.

A coordinate plane is a two-dimensional surface formed by two perpendicular lines, the x-axis (horizontal) and the y-axis (vertical). This plane allows you to graph and visualize the relationships between ordered pairs.

To plot \((-2, 5)\) on a coordinate plane:

• Start at the origin (0,0).
• Move 2 units to the left (along the x-axis).
• Move 5 units up (along the y-axis).

You will end up at point \((-2, 5)\). Visualizing points on the coordinate plane helps in understanding solutions to equations, as it shows whether points lie on the line represented by the equation.

Substitution is a technique used in algebra to determine if an ordered pair is a solution to an equation. Substitution involves replacing variables with their corresponding values from the ordered pair.

In our exercise, we substitute x with -2 and y with 5 in the equation \(2x - y = -9\):
\[ 2(-2) - 5 = -9 \]
Perform the calculations step-by-step:

• Multiply 2 by -2, resulting in -4.
• Subtract 5 from -4, resulting in -9.

Since both sides of the equation are equal after substitution, \((-2, 5)\) is indeed a solution to the equation \(2x - y = -9\).