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Question: Solve the system by substitution: 3x- y = 3, -6x + 2y = -6


A ) No solution
B ) Infinitely many solutions
C ) (2, 3)
D ) (1, 0)

Steps to derive

1 3x - y = 3
 [First equation.]

2 -y = 3 - 3x
 [Subtract 3x from each side.]

3 y = -3 + 3x
 [Multiply with -1 from each side.]

4 -6x + 2y = -6
 [Second equation.]

5 -6x + 2(-3 + 3x) = -6
 [Substitute y in second equation.]

6 -6x - 6 + 6x = -6

7 -6 = -6, which is true for all x, y.

8 So, every ordered pair that satisfies one equation satisfies the other equation.

9 So, the system has infinitely many solutions.



Hence the right answer is Option B

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