$\mathrm{H} 45 \mathrm{a}$ KUMO Jimultaneous Equations with Two Variables 3 \begin{tabular}{|c|c|c|c|c|} \hline $\mathbf{1 0 0} \%$ & $\sim 90 \%$ & $\sim 80 \%$ & $\sim 70 \%$ & $69 \%$ \\ \hline (mistakes) 0 & - & - & 1 & 2 \\ \hline \end{tabular} Solve the following simultaneous e (1) \[ \left\{\begin{array}{l} 2 x+3 y=1.9 \\ 3 x+y=1.1 \end{array}\right. \] $20 x+30 y=19$ $30 x+10 y=11$

Step 1 ：The given problem is a system of linear equations. We can solve this system using various methods such as substitution, elimination or matrix method. Here, I will use the elimination method.

Step 2 ：The system of equations is: \[\left\{\begin{array}{l} 2 x+3 y=1.9 \\ 3 x+y=1.1 \end{array}\right.\]

Step 3 ：To make the coefficients of y the same in both equations, I will multiply the first equation by 10 and the second equation by 30. This will give us: \[\left\{\begin{array}{l} 20 x+30 y=19 \\ 90 x+30 y=33 \end{array}\right.\]

Step 4 ：Now, we can subtract the second equation from the first to eliminate y and solve for x. Then, we can substitute x into one of the original equations to solve for y.

Step 5 ：The solution to the system of equations is x = 1/5 and y = 1/2. This means that the value of x that satisfies both equations is 1/5 and the value of y that satisfies both equations is 1/2.

Step 6 ：Final Answer: The solution to the system of equations is \(\boxed{x = \frac{1}{5}, y = \frac{1}{2}}\).