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Question: Solve the system by substitution:
4x - 2y = 6
- 10x + 5y = - 15


A ) (2, 0)
B ) (2, 3)
C ) Infinite solutions
D ) No solution

Steps to derive

1 4x - 2y = 6
 [First equation.]

2 - 2y = 6 - 4x
 [Subtract 4x from the two sides of the equation.]

3 y = - 3 + 2x
 [Divide through out by - 2 from each side.]

4 - 10x + 5y = - 15
 [Second equation.]

5 - 10x + 5(- 3 + 2x) = - 15
 [Substitute the values.]

6 - 10x - 15 + 10x = - 15

7 - 15 = - 15

8 The above equation is always true, the number of solutions is infinite.

9 The solution is { (x, y): 4x - 2y = 6 }.



Hence the right answer is Option C

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