91Ó°ÊÓ

Ordered pairs are fundamental in understanding the coordinate system in mathematics. They are written in the form

• (x, y), where 'x' is the first component, and 'y' is the second component.
• The 'x' value represents the position along the horizontal axis (commonly referred to as the x-axis).
• The 'y' value represents the position along the vertical axis (commonly referred to as the y-axis).

Ordered pairs are used to pinpoint the location of a point on the Cartesian plane. Consider each ordered pair as a roadmap to find specific points in a two-dimensional space. If you know the ordered pair, you can easily locate where the point lies by moving horizontally to the 'x' value and vertically to the 'y' value.
In our exercise, the ordered pair initially contains the 'x' value, 2, and we solve to find 'y'. This practice helps in visualizing and understanding how linear equations represent lines on a graph.

To solve for 'y' in a linear equation, you typically isolate 'y' on one side equation. The equation given in the exercise is:

• y = 6x - 7

When you're provided with an 'x' value, like 2 in the example given, the next step is to calculate the corresponding 'y' value. Here's how you approach it:1. **Substitute the given x-value**: Plug the provided 'x' value into the equation. For our exercise, it involves substituting x = 2: \( y = 6(2) - 7 \) 2. **Perform the calculation**: Multiply 6 by 2, giving us 12, then subtract 7 to solve for 'y': \( y = 12 - 7 = 5 \)
By following these steps, you have successfully found 'y'. Solving for 'y' constructs the missing part of your ordered pair, completing the point's coordinates.

The substitution method is a straightforward way of solving equations by replacing variables with given values. Let's explore how this process aids in solving linear equations efficiently. Here's a simple guide:- **Identify what's known**: In our problem, the 'x' value is provided as 2. - **Substitute the known value**: Replace 'x' in the equation with this known value. For example, when x = 2, it changes the equation from \( y = 6x - 7 \) to \( y = 6(2) - 7 \).- **Simplify the equation**: After substitution, carry out the arithmetic operations to find 'y'.This method is incredibly useful because it transforms an equation with variables into a simple arithmetic problem. By following these steps, you can quickly and accurately determine the solution. In our example, completing the substitution and solving yielded the ordered pair (2, 5), marking the exact point on the coordinate plane.