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. How many solutions does this system of equations have? Explain how you know. 9x – 3y = -6 5y=15x+10

User Dax Durax
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1 Answer

6 votes

Answer:

No unique solution or alternatively

An infinite number of solutions

Explanation:

Consider the two equations:

9x – 3y = -6 [1]

5y = 15x + 10 [2]

For equation [2] subtract 15x from both sides to get the x terms on the LHS:

- 15x + 5y = 1 [3]

Divide Equation [1] by 3:
3x - y = -2 [4]

Divided Equation [3] by 5

-3x + y = 2 [5]

Multiply Eq[5] by -1 to get
3x - y = -2 [6]

Since both equations [5] and [6] are the same, the original equations [1] and [2] are also the same and therefore we have a single equation in two variables which does not have a unique solution.

Therefore there is no unique solution or alternatively there are an infinite number of solutions

User Ricardo Felgueiras
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