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Absolutely, but only if they're concurrent. This means that they not only share the same slope, but also share the same y-intercept, which results in the lines sharing every x-y coordinate. Concurrent is another way of saying the lines are actually just the same line. If they're not concurrent, then they're only parallel, so will have no solutions. For example:
Our system:
2x + 3y = 6
4x + 6y = 12
These two equations, when you put them in slope-intercept form, will have the same slope and the same y-intercept. This means they are concurrent, and their system will have infinitely many solutions. Notice that if you multiply the entire first equation by 2, you get the second equation. Concurrent lines always share this kind of relationship, where you can multiply one by some number to get the other.
Another system:
2x + 3y = 6
4x + 6y = 10
These two equations, when you put them in slope-intercept form, will have the same slope but will not have the same y-intercept. This means they are parallel, so their system will have no solutions. Notice that if you multiply the entire first equation by 2, the coefficients on x and y will be the same in both equations, but the constants on the right side will not. This relationship is shared by all parallel lines.
What else can I help you with?
Does every pair of linear simultaneous equations have a solution?
Actually not. Two linear equations have either one solution, no solution, or many solutions, all depends on the slope of the equations and their intercepts. If the two lines have different slopes, then there will be only one solution. If they have the same slope and the same intercept, then these two lines are dependent and there will be many solutions (infinite solutions). When the lines have the same slope but they have different intercept, then there will be no point of intersection and hence, they do not have a solution.
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
what- use the slopes and y- intercept of the lines to determine the number of solutions to the system?
consistent dependent
What are the slopes of perpendicular lines called?
Slopes of line perpendicular to the x-axis are undefined.
As slopes of x and y axes are 0 and undefined respectively why the product of slopes of x and y axes is -1?
1
Does the graph of a system of equations with different slopes have no solutions?
The graph of a system of equations with the same slope will have no solution, unless they have the same y intercept, which would give them infinitely many solutions. Different slopes means that there is one solution.
When equations of linear systems have different slopes how many solutions does it have?
One solution
When graphing a system of equations with infinitely many solutions the slopes of the two lines will be?
When graphing a system of equations with infinitely many solutions, the slopes of the two lines will be equal, as they represent the same line. Additionally, the lines will coincide, meaning every point on one line is also a point on the other. This occurs when both equations are essentially the same, differing only by a constant factor.
How many solutions would you expect for this system of equations?
To determine the number of solutions for a system of equations, one would typically analyze the equations' characteristics—such as their slopes and intercepts in the case of linear equations. If the equations represent parallel lines, there would be no solutions; if they intersect at a single point, there is one solution; and if they are identical, there would be infinitely many solutions. Without specific equations, it's impossible to provide a definitive number of solutions.
Systems of equations with different slopes and different y-intercepts have no solutions?
No the only time that a system of equations would have no solutions is when the two equations have the same slope but different y-intercepts which would mean that they are parallel lines. However, if they have different slopes and different y-intercepts than the solution would be where the two lines intersect.
Can you determine whether a system of two linear equations has one solution an infinite number of solutions or no solution by simply?
Yes, you can determine the nature of a system of two linear equations by analyzing their slopes and intercepts. If the lines represented by the equations have different slopes, the system has one solution (they intersect at a single point). If the lines have the same slope but different intercepts, there is no solution (the lines are parallel). If the lines have the same slope and the same intercept, there are infinitely many solutions (the lines coincide).
Can systems of equations with the same slopes and different y-intercepts have no solution?
It is a correct statement.
How do you know if a system has one solution?
If the equations or inequalities have the same slope, they have no solution or infinite solutions. If the equations/inequalities have different slopes, the system has only one solution.
What is the different kinds of linear system according to slope?
The question makes little general sense because the concept of slopes is appropriate when dealing with equations in only two variables.Assuming, therefore, that there are only two variables, then either the slopes are the same or they are different,If the slopes are the same and the intercepts are the same: there are infinitely many solutionsIf the slopes are the same and the intercepts are different: there are no solutionsIf the slopes are different: there is a unique solution.
Does every pair of linear simultaneous equations have a solution?
Actually not. Two linear equations have either one solution, no solution, or many solutions, all depends on the slope of the equations and their intercepts. If the two lines have different slopes, then there will be only one solution. If they have the same slope and the same intercept, then these two lines are dependent and there will be many solutions (infinite solutions). When the lines have the same slope but they have different intercept, then there will be no point of intersection and hence, they do not have a solution.
A system of two linear equations has exactly one solution if?
The slopes (gradients) of the two equations are different.
Does the system of equations have no solution one solution or infinitely many solutions y plus x equals 4 y - 4 equals x?
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