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Solve the system by substitution.

[tex]\[
\begin{array}{l}
x = 3y \\
4x - 12y = 4
\end{array}
\][/tex]

Select the correct choice below and, if necessary, fill in the answer box to complete your choice:

A. The solution set is [tex]\(\square\}. \)[/tex] (Type an ordered pair.)

B. There are infinitely many solutions.

C. There is no solution.



Answer :

GinnyAnswer
To solve the system of equations by substitution, we can follow these steps:

### Given Equations:

1. [tex]\( x = 3y \)[/tex]
2. [tex]\( 4x - 12y = 4 \)[/tex]

### Step-by-Step Solution:

1. Substitute [tex]\( x \)[/tex] from Equation 1 into Equation 2:

Since [tex]\( x = 3y \)[/tex], we can substitute [tex]\( x \)[/tex] in the second equation [tex]\( 4x - 12y = 4 \)[/tex].

4(3y) - 12y = 4

2. Simplify the equation:

Distribute [tex]\( 4 \)[/tex] in the equation:

12y - 12y = 4

Simplify by combining like terms:

0 = 4

This is a contradiction because 0 is not equal to 4.

3. Analyze the result:

The contradiction indicates that there is no pair of [tex]\( (x, y) \)[/tex] that satisfies both equations simultaneously.

### Conclusion:

Therefore, the system of equations has no solution.

The correct choice is:
C. There is no solution.

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