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what- use the slopes and y- intercept of the lines to determine the number of solutions to the system?
which of these describes the type of system above
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If two lines intercept exactly at one point each of their slopes are?
unequal.
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.
Does every line have a slope intercept equation?
No. Vertical lines and horizontal lines have undefined and 0 slopes. Undefined could be any number, so the answer is No. Good luck with your Apex :)
Write an equation of the line that has a slope of -7 and y intercept 6 in slope intercept form?
Use the slope-intercept form of the line: y = mx + b Here, "m" is the slope, and "b" is the y-intercept, so just replace these variables with the corresponding slope and intercept - and you got your equation. And PLEASE don't ask lots of almost-identical questions, with different slopes and y-intercept. It is really easy to replace the slope and the intercept in this equation.
Can systems of equations with the same slopes have infinitely many solutions?
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 = 64x + 6y = 12These 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 = 64x + 6y = 10These 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- use the slopes and y- intercepts of he lines to determine the number of solutions to the system?
inconsistent
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.
How can you use the slopes and y-intercepts to determine if two lines are parallel?
If the lines are straight and have the same slope they are parallel, no matter what the y intercept is
Describe slope and y intercept of intersecting lines?
To intersect, their slopes have to be different. The y-intercept can be anything.
How wold you classify two linear equations have the same y-intercept and different slopes?
Two linear equations (or lines) with the same y-intercept and different slopes are intersecting lines. They intersect at the y-intercept. If the slopes are negative reciprocals (ex: one slope is 3 and one slope it -1/3) then they are perpendicular lines.
Two lines that have different slopes but the same y-intercept?
no solution
How do parallel and perpendicular slopes compare or their y intercept?
There is no relationship between the slopes of parallel or perpendicular lines and their y-intercepts.
If two lines intercept exactly at one point each of their slopes are?
unequal.
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.
Will two lines with different y intercept cross each other?
They will, if they have different slopes.
Imagine that you are given two linear equations in slope-intercept form. You notice that the slopes are different but the y-intercepts are the same. How many solutions would you expect for this system?
infinintly many. for apex.
Does every line have a slope intercept equation?
No. Vertical lines and horizontal lines have undefined and 0 slopes. Undefined could be any number, so the answer is No. Good luck with your Apex :)
