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Use the substitution method to determine the solution type of the following system.

3y - 6x = 3
y = 2x + 1
a. No solutions
b. 0 Infinitely many solutions
c. 0 (3,-1)
d. (2,0)

1 Answer

3 votes

Final answer:

Upon substituting y from one equation into the other, we find the statement 3 = 3, indicating the two equations represent the same line, thus the system has infinitely many solutions.

Step-by-step explanation:

In order to determine the solution to the given system of equations using the substitution method, we will substitute the value of y from the second equation into the first equation. The second equation is given as y = 2x + 1. Substituting 2x + 1 for y in the first equation, 3y - 6x = 3, gives: 3(2x + 1) - 6x = 3. Simplifying this, we get 6x + 3 - 6x = 3, which further simplifies to 3 = 3. This is a true statement regardless of the value of x, indicating that the two equations are essentially the same line, resulting in infinitely many solutions.

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