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5 votes
Solve the system of equations:

x - 3y = 9
-x + 3y = -9
A. (–5, 6)
B. (5, –6)
C. Infinite solutions
D. No solutions

User Tomzie
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7.8k points

1 Answer

7 votes

Final answer:

The system of equations given are actually the same line and every point on this line is a solution, which means the correct answer is C. Infinite solutions.

Step-by-step explanation:

The system of equations given to solve is:

  • x - 3y = 9
  • -x + 3y = -9

By adding the two equations, we can eliminate both x and y because they are additive inverses of each other. When we add them, we get:

x - 3y - x + 3y = 9 - 9

Which simplifies to:

0 = 0

This is an identity, meaning that the two equations are actually the same line, and therefore every point on the line is a solution. Thus, the correct answer is C. Infinite solutions.

User Gustavo Gondim
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7.7k points