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A **system of equations** consists of two or more equations with the same set of variables. In many cases, these equations are linear, meaning they graph as straight lines on a coordinate plane. Solving a system of linear equations involves finding the point or points where these lines intersect, which means finding a set of values for the variables that satisfies all the equations simultaneously.

Here are some essential properties of systems of linear equations:

• If two lines intersect at one point, there is a unique solution to the system of equations.
• If the lines are parallel and don't intersect, there is no solution to the system.
• If the lines are coincident (overlap completely), there are infinitely many solutions.

In the given exercise, the solution (3, -4.5) is the intersection point of two lines, meaning the equations in the system intersect at this point.

**Coordinate geometry**, also known as analytic geometry, involves the study of geometric figures through the coordinate plane. It brings algebra and geometry together by describing geometric figures numerically and solving geometric problems with algebra.

The coordinate plane is defined by two perpendicular axes: the x-axis (horizontal) and the y-axis (vertical). Any point on this plane is represented by an ordered pair (x, y), where (x) is the distance from the y-axis, and (y) is the distance from the x-axis. This is the basis for expressing the position of points, lines, and shapes algebraically.

For instance, the solution point (3, -4.5) in the exercise can be plotted on the coordinate plane, showing its exact location and allowing us to understand the geometrical significance of other shapes and lines in relation to this point.

The **equation of a line** in coordinate geometry represents all the points on that line in the coordinate plane. There are several forms to express linear equations:

• The slope-intercept form: (y = mx + c), where (m) is the slope and (c) is the y-intercept.
• The point-slope form: (y - y_1 = m(x - x_1)), used when the slope and one point on the line are known.
• The standard form: (Ax + By = C), where (A), (B), and (C) are constants.

For special cases like horizontal and vertical lines, their equations simplify drastically:

• A horizontal line, where (y) is constant, has the equation (y = b).
• A vertical line, where (x) is constant, has the equation (x = a).

In the given exercise, the horizontal line through the solution point (3, -4.5) is represented by (y = -4.5), and the vertical line is represented by (x = 3). These equations clearly illustrate the simplicity and utility of coordinate geometry in pinpointing line positions relative to specific points.