Question 825817: Given the equation, 3x + 9y = -8, write a second linear equation to create a system that :
Has exactly one solution. Explain your reasoning.
Has no solution. Explain your reasoning.
Has infinitely many solutions. Explain your reasoning.
Part 2 :
Interpret the meaning of the solution, if it exists, in the context of the graph of the following system of equations.
{ -5x + 2y = 10
{10x - 4y = -20
Found 2 solutions by richwmiller, stanbon:
Answer by richwmiller(17219)   (Show Source):
Answer by stanbon(75887)  (Show Source):
You can put this solution on YOUR website! Given the equation, 3x + 9y = -8, write a second linear equation to create a system that :
Has exactly one solution.
3x-9y=-8
Explain your reasoning.
The 1st has slope = -1/3
The 2nd has slope = 1/3
So the graphs intersect at one point:
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Has no solution.
3x + 9y = 2
Explain your reasoning.
Both have the same slopes of -1/3 but different y-intercepts
So the graphs do not intersect.
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Has infinitely many solutions.
6x + 18y = -16
Explain your reasoning.
One is a multiple of the other.
The graphs are the same line; they intersect at every point.
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Part 2 :
Interpret the meaning of the solution, if it exists, in the context of the graph of the following system of equations.
{ -5x + 2y = 10
{10x - 4y = -20
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Infinite number of solutions because
the lower is -2 times the upper equation.
They intersect at every point.
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Cheers,
Stan H.
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