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By looking at two linear equations how can you tell that the corresponding lines are parallel?
By looking st two linear equations you can tell that the corresponding lines are parallel when the slope is the same. The slope controls where the line is.
If two linear equations are in standard form how can you tell that the graphs are parellel?
If the slopes are the same on both graphs, they are parallel, and will never touch.
What is true about a system of two linear equations that has no solution?
The two equations represent parallel lines.
How do you identify two linear equations that are parallel using slopes of two lines?
Two linear equations that are parallel with have the sameslope, or the m value in y = mx + b will be the same.For example, y = 3x + 5 is parallel to y = 3x - 6
If a system of linear equations has no solution then the graph of the two equationsmust be what kind of line?
parallel
How can you tell if two equations are parallel?
if they have the same slope If two linear equations are inconsistent - that is, have no solution, then the graphs would be parallel and have the same slope if their slope is defined. Example: x + y = 1 x + y = 2 Example with no slope: x = 1 x = 2
How can we tell if two lines are parallel perpendicular or neither just from their equations?
If the slope of the equations are the same then they are parallel If the slope of the equations are minus reciprocal then they are perpendicular If the slope of the equations are different then they are neither
Is it possible for a system of linear equations to have zero solutions?
Yes, a system of linear equations can have zero solutions, which is known as an inconsistent system. This occurs when the equations represent parallel lines that never intersect, meaning there is no point that satisfies all equations simultaneously. A common example is the system represented by the equations (y = 2x + 1) and (y = 2x - 3), which are parallel and thus have no solutions.
Can a system of linear equations have no solution?
Yes, a system of linear equations can have no solution, which occurs when the equations are inconsistent. This typically happens when the lines represented by the equations are parallel, meaning they have the same slope but different y-intercepts. As a result, they never intersect, indicating that there are no values for the variables that satisfy all equations simultaneously.
What is the definition of Simultaneous Linear Equations?
A system of linear equations is two or more simultaneous linear equations. In mathematics, a system of linear equations (or linear system) is a collection of linear equations involving the same set of variables.
What makes two linear equations either parallel or perpendicular to each other?
Depending on the value of the slope or gradient if its the same then they are parallel if its a reciprocal then they are perpendicular.
Can a system of two linear equations have exactly two solutions explain?
No, a system of two linear equations cannot have exactly two solutions. In a two-dimensional space, two linear equations can either intersect at one point (one solution), be parallel (no solutions), or be the same line (infinitely many solutions). Therefore, it is impossible for a system of two linear equations to have exactly two solutions.
