Equation of a Line Completing System with 3x - 2y = 8

In summary, the equation of a line completing system is a mathematical method used to find the equation of a line passing through two given points. It involves using the slope-intercept form (y = mx + b) and solving for the unknown values of slope and y-intercept. This can be done by either substitution or elimination methods. The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. The equation 3x - 2y = 8 is a linear equation that can be rearranged into the slope-intercept form to represent the equation of a line. However, the equation of a line completing system cannot be used for non-linear equations, as they
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Q: Write an equation of a line that forms a system with the equation 3x - 2y = 8 that has infinitely solutions.
A: 3x - 2y = 8.
I believe this to be correct because it makes an identical line to one of her correct answers (6x - 4y = 16) and nowhere did it specify that it had to be new. Could you tell me my mistake?
 
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Did you really think that your teacher intended you to just copy what she had written? On a technical level repeating the same equation does NOT give a "system".
 

1. What is the equation of a line completing system?

The equation of a line completing system is a set of two or more equations that can be solved simultaneously to find the coordinates of the point where the lines intersect.

2. How many equations are needed to complete a system?

At least two equations are needed to complete a system. However, in some cases, more equations may be required to accurately solve for the coordinates of the intersection point.

3. What is the standard form of an equation of a line?

The standard form of an equation of a line is Ax + By = C, where A, B, and C are constants and x and y are variables.

4. How can I solve for the coordinates of the intersection point using the equation 3x - 2y = 8?

To solve for the coordinates of the intersection point, you can use the substitution method or the elimination method. In the substitution method, you can solve for one variable in terms of the other and then substitute that value into the other equation. In the elimination method, you can add or subtract the equations to eliminate one of the variables and then solve for the remaining variable.

5. What is the significance of the slope and y-intercept in the equation 3x - 2y = 8?

The slope and y-intercept in the equation 3x - 2y = 8 represent the characteristics of the line. The slope (m) represents the steepness of the line, and the y-intercept (b) represents the point where the line crosses the y-axis. These values can be used to graph the line and determine its direction and position on the coordinate plane.

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