Solve by Substitution x+3y=2 , 3x+9y=6

Problem

{[x+3*y=2],[3*x+9*y=6])

Solution

1. Isolate the variable x in the first equation by subtracting 3*y from both sides.

x=2−3*y

2. Substitute the expression for x into the second equation.

3*(2−3*y)+9*y=6

3. Distribute the 3 into the parentheses.

6−9*y+9*y=6

4. Combine like terms on the left side of the equation.

6=6

5. Interpret the result. Since the statement 6 = 6$ is always true and the variables have been eliminated, the two equations represent the same line. This means there are infinitely many solutions.

Final Answer

Infinitely many solutions

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