$\mathrm{H} 45 \mathrm{a}$ KUMON Stmultaneous Equations with Two Variables 3 \begin{tabular}{|c|c|c|c|c|} \hline $100 \%$ & $\sim 90 \%$ & $\sim 80 \%$ & $\sim 70 \%$ & $69 \%$ \\ \hline (mistakes) 0 & - & - & 2 \\ \hline \end{tabular} Solve the following simultaneous equati (1) $\left\{\begin{array}{l}2 x+3 y=1.9 \\ 3 x+y=1.1\end{array}\right.$ (
Solution
Step 1 ：The system of equations given is: \[\begin{align*} 2x + 3y &= 1.9 \\ 3x + y &= 1.1 \end{align*}\]
Step 2 ：We can solve this system of equations using the elimination method. First, we multiply the first equation by 3 and the second equation by 2 to make the coefficients of y the same in both equations. This gives us: \[\begin{align*} 6x + 9y &= 5.7 \\ 6x + 2y &= 2.2 \end{align*}\]
Step 3 ：Next, we subtract the second equation from the first to eliminate y. This gives us: \[\begin{align*} 0x + 7y &= 3.5 \end{align*}\] Simplifying this equation gives us: \[\begin{align*} y &= 0.5 \end{align*}\]
Step 4 ：After finding y, we can substitute it into either of the original equations to find the value of x. Substituting y = 0.5 into the first equation gives us: \[\begin{align*} 2x + 3(0.5) &= 1.9 \\ 2x + 1.5 &= 1.9 \\ 2x &= 0.4 \\ x &= 0.2 \end{align*}\]
Step 5 ：The solution to the system of equations is \(x = \boxed{0.2}\) and \(y = \boxed{0.5}\). These values of x and y satisfy both equations simultaneously.
