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МатематикаВопрос:
Solve the system of equations: {5y = x - 1, 7y = 4x - 4.
Ответ:
Let's solve the system of equations:
We have the following system:
\[\begin{cases} 5y = x - 1 \\ 7y = 4x - 4 \end{cases}\]Краткое пояснение: We'll solve for \(x\) in the first equation and substitute it into the second equation to solve for \(y\). Then, we'll substitute the value of \(y\) back into the first equation to solve for \(x\).
Пошаговое решение:
- From the first equation, solve for \(x\):
- Substitute this expression for \(x\) into the second equation:
- Simplify and solve for \(y\):
- Now substitute \(y = 0\) back into the equation \(x = 5y + 1\) to find \(x\):
\[5y = x - 1 \implies x = 5y + 1\]
\[7y = 4(5y + 1) - 4\]
\[7y = 20y + 4 - 4 \implies 7y = 20y \implies 13y = 0 \implies y = 0\]
\[x = 5(0) + 1 \implies x = 1\]
Answer: x = 1, y = 0
