Answered

Use a graphing calculator to solve the system. Express solutions with approximations to the nearest thousandth.

[tex]\[
\begin{array}{l}
\frac{7}{3} x + y = 0.4 \\
0.6 x - y = 3
\end{array}
\][/tex]

The solution set is [tex]$\square$[/tex].
(Type an ordered pair. Round to the nearest thousandth as needed.)



Answer :

GinnyAnswer
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]

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