Solve the system of equations: [7x-5y-4=0, 10y = 14x+3.

Question

Вопрос:

Solve the system of equations: [7x-5y-4=0, 10y = 14x+3.

Ответ:

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Accepted Answer

Let's solve the system of equations:

\[\begin{cases}7x - 5y - 4 = 0 \\10y = 14x + 3\end{cases}\]

First, we can rewrite the equations to make them easier to work with:

\[\begin{cases}7x - 5y = 4 \\14x - 10y = -3\end{cases}\]

Краткое пояснение: We will solve this system using the substitution or elimination method. Here, the elimination method looks easier since we can multiply the first equation by a constant to match the coefficients of either x or y in the second equation.

Пошаговое решение:

Шаг 1: Multiply the first equation by 2 to make the coefficient of x equal to 14:

\[2(7x - 5y) = 2(4)\]

\[14x - 10y = 8\]

Шаг 2: Now we have the following system:

\[\begin{cases}14x - 10y = 8 \\14x - 10y = -3\end{cases}\]

Шаг 3: Subtract the second equation from the first equation:

\[(14x - 10y) - (14x - 10y) = 8 - (-3)\]

\[0 = 11\]

This statement is false, meaning there is no solution to this system of equations because the lines are parallel.

Answer: No solution. The system is inconsistent.