Question

solve the system of equation using the addition/elimination method.
x + 3y = 2
3x + 9y = 6
no solution
infinite solution
(3, 1/3)
(9, 6)

Explanation:

Step1: Analyze the equations

The system is:
\(x + 3y = 2\) ---(1)
\(3x + 9y = 6\) ---(2)

Notice that equation (2) can be simplified by dividing both sides by 3.

Step2: Simplify equation (2)

Divide equation (2) by 3: \(\frac{3x + 9y}{3}=\frac{6}{3}\), which gives \(x + 3y = 2\), which is the same as equation (1).

This means the two equations represent the same line, so there are infinite solutions.

Answer:

Infinite Solution