Explain (in 3 or more sentences) how you can tell if a system of two linear equations has 0, 1, or infinitely many solutions. Be sure to say how the lines are not related and give specific examples of each.
ok, I think it might be:
A system of two linear equations has one ordered pair if the lines intersect. It has no ordered pairs if the two lines do not intersect. It has an infinite number of ordered pairs if the two lines are the same.
Is this right? Is there anything else I need to add?
Now I just need to give specific examples of each... so do I need to make up 3 problems and then graph them?
No. If they never meet, there is no solution. If they cross at one point, one solution. If the lines are colinear(that is the same line), the solutions are infinite.
What are some facts about linear lines
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Here are some facts about linear lines:
1. Linear lines have a constant slope. The slope represents the rate of change between the x and y coordinates.
2. Two linear lines are parallel if they have the same slope but different y-intercepts. Parallel lines never intersect and have no solution when solved as a system of equations.
3. Two linear lines are perpendicular if their slopes are negative reciprocals of each other. Perpendicular lines intersect at a 90-degree angle and have one solution when solved as a system of equations.
4. A linear line can be determined using only two points on the line. By using the slope-intercept form equation (y = mx + b), where m is the slope and b is the y-intercept, we can determine the equation of a line.
5. Linear lines are often represented graphically as straight lines. The slope determines the steepness of the line, whether it is increasing or decreasing, and the direction (positive or negative) of the line on a coordinate plane.
These facts can help us analyze and understand the behavior and characteristics of linear lines.