SOLUTION: I got a question I hardly understand let alone solve. What value of m gives a system y=1^2 x-2 y=mx-1 with a) one solution b) an infinitely many solutions c) no solution

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I got a question I hardly understand let alone solve.
What value of m gives a system
y=1^2 x-2
y=mx-1 with
a) one solution
b) an infinitely many solutions
c) no solution
There are three possibilities when solving linear equations (that one you gave is linear): one solution, infinitely many, or no solution
One solution exists when the graph is intersecting lines.
No solution exists when the graph is parallel lines.
Infinite solutions exists when the graph is coincident lines.
Let's go back.
y=1^2 x-2 >>>I'm confused. I'll assume it's
Since the equation is in the slope intercept form (y=mx+b), the slope of this line is 1/2.
For the line to intersect but not coincide, the slope of the second line must not be 1/2.
Therefore, the equations have one solution when, m is not equal to 1/2.Ans.
b) Two lines are coincident when they have the same slope and y-intercepts. The y-intercepts of you given lines are -2 and -1, which can never be equal.
Therefore, no value of m would make the system have infinite solutions.
c) Two equations have no solutions when their graphs are parallel, i.e, same slope but diff. y-intercepts.
Since their intercepts are -2 and -1. This system is possible.
Also, the lines must have the same slope.
Therefore, m=1/2 will make the system have no solution.

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