Muriel says she has written a system of two linear equations that has an infinite number of solutions. One of the equations of t
he system is 3y = 2x – 9. Which could be the other equation?
2 answers:
A system of equations with infinitely many solutions is a system where the two equations are identical. The lines coincide. Anything that is equal to 
will work. You could try multiply the entire equation by some number, or moving terms around, or adding terms to both sides, or any combination of operations that you apply to the entire equation.
You could multiply the whole thing by 4.5 to get
. If you want, you could mix things up and write it in slope-intercept form: 
. The point is, anything that is equivalent to the original equation will give infinitely many solutions x and y. You can test this by plugging in values x and y and seeing the answers!
The attached graph shows that four different equations are really the same.
You could multiply the whole thing by 4.5 to get
The attached graph shows that four different equations are really the same.
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So here are the rules of horizontal asymptotes:
- Degree of Numerator > Degree of Denominator: No horizontal asymptote
- Degree of Numerator = Degree of Denominator:
- Degree of Numerator < Degree of Denominator: y = 0
Looking at the rational function, since the degree of the numerator is 2 and the degree of the denominator is 1 (and 2 > 1), this means that <u>this function has no horizontal asymptote.</u>