Question 174865
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 <b>intersecting</b> lines.
No solution exists when the graph is <b>parallel</b> lines.
Infinite solutions exists when the graph is </b>coincident</b> lines.

Let's go back.

y=1^2 x-2   >>>I'm confused. I'll assume it's {{{y=(1/2)x-2}}}

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 <b>the same slope and y-intercepts</b>. 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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