Problem

Solve the system by the method of your choice. \[ \begin{array}{l} 4 x+3 y=5 \\ 8 x+6 y=10 \end{array} \] Select the correct choice below and, if nocessary, fill in the answer box within your choice. A. The solution set is (Type an ordered pair.) B. There are infinitely many solutions. The solution set is $\{(x, y)\}$ (Simplify your answer. Type an equation. Use integers or fractions for any numbers in the equation.) C. There is no solution. The solution set is $\varnothing$.

Solution

Step 1 :The system of equations is: \[\begin{array}{l} 4 x+3 y=5 \\ 8 x+6 y=10 \end{array}\]

Step 2 :We can see that the second equation is just the first equation multiplied by 2. This means that the two equations are not independent, they are the same line.

Step 3 :Therefore, there are infinitely many solutions that satisfy both equations.

Step 4 :The solution set is \(\{(x, y)\}\) where \(x = \frac{5}{4} - \frac{3y}{4}\).

Step 5 :\(\boxed{\text{Final Answer: The correct choice is B. There are infinitely many solutions. The solution set is }\{(x, y)\}\text{ where }x = \frac{5}{4} - \frac{3y}{4}\}

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Source: https://solvelyapp.com/problems/18172/

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