To solve the system of equations:
[tex]\[
\begin{array}{l}
\frac{7}{3} x + y = 0.4 \\
0.6 x - y = 3
\end{array}
\][/tex]
we follow these steps:
1. Rewrite the equations for better visualization:
Equation 1: \(\frac{7}{3} x + y = 0.4\)
Equation 2: \(0.6 x - y = 3\)
2. Isolate \(y\) in Equation 2:
[tex]\[
y = 0.6 x - 3
\][/tex]
3. Substitute \(y\) from Equation 2 into Equation 1:
[tex]\[
\frac{7}{3} x + (0.6 x - 3) = 0.4
\][/tex]
4. Combine like terms and simplify:
[tex]\[
\frac{7}{3} x + 0.6 x - 3 = 0.4
\][/tex]
Convert \(0.6 x\) to a fraction to combine with \(\frac{7}{3} x\):
[tex]\[
\frac{7}{3} x + \frac{6}{10} x - 3 = 0.4
\][/tex]
Simplify \(\frac{6}{10}\) to \(\frac{3}{5}\):
[tex]\[
\frac{7}{3} x + \frac{3}{5} x - 3 = 0.4
\][/tex]
Find a common denominator for the fractions:
[tex]\[
\frac{35}{15} x + \frac{9}{15} x - 3 = 0.4
\][/tex]
Combine the fractions:
[tex]\[
\frac{44}{15} x - 3 = 0.4
\][/tex]
5. Solve for \(x\):
Add 3 to both sides:
[tex]\[
\frac{44}{15} x = 3.4
\][/tex]
Multiply both sides by \(\frac{15}{44}\):
[tex]\[
x = \frac{3.4 \times 15}{44}
\][/tex]
Simplify:
[tex]\[
x \approx 1.159
\][/tex]
6. Substitute \(x\) back into Equation 2 to find \(y\):
[tex]\[
y = 0.6 (1.159) - 3
\][/tex]
Calculate:
[tex]\[
y \approx 0.6954 - 3
\][/tex]
So:
[tex]\[
y \approx -2.305
\][/tex]
Therefore, the solution to the system of equations is:
[tex]\(\boxed{(1.159, -2.305)}\)[/tex]
