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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.
