Question

Solve the linear system. $$ \begin{aligned} &3 x+9 y=1\\\ &2 x+3 y=\frac{2}{3} \end{aligned} $$

Short answer

The solution to the system of equations is \(x = 1/3\) and \(y = 0\).

Step-by-step solution

- Simplify the equations

The equations \(3x + 9y = 1\) and \(2x + 3y = 2/3\) can be simplified by their common divisors. The simplified system of equation is: \[\begin{cases} x + 3y = 1/3\ 2x + 3y = 2/3 \end{cases} \]

- Subtraction

Subtract the first equation from the second equation. This results in \( x = 1/3 \)

- Subtitution

Substitute \( x = 1/3 \) in the first equation: \(1/3 + 3y = 1/3\), which simplifies to \(y = 0\)

- Summary of the solution

So the solution of the system is \(x = 1/3, y = 0\)