Questions: Используя метод подстановки, решите систему линейных уравнений: 3x - 8y = 99 4y = -32x - 16. Выразите y из второго уравнения: 3x - 8y = 99 y = и найдите решение системы линейных уравнений. x= , y= .

Используя метод подстановки, решите систему линейных уравнений: 3x - 8y = 99 4y = -32x - 16. Выразите y из второго уравнения: 3x - 8y = 99 y = и найдите решение системы линейных уравнений. x= , y= .
Transcript text: Используя метод подстановки, решите систему линейных уравнений: \[ \left\{\begin{aligned} 3 x-8 y & =99 \\ 4 y & =-32 x-16 . \end{aligned}\right. \] Выразите $y$ из второго уравнения: \[ \left\{\begin{array}{l} 3 x-8 y=99 \\ y= \end{array}\right. \] и найдите решение системы линейных уравнений. \[ x=\square, y=\square . \]
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Solution

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Solution Steps

Step 1: Write the System of Equations

We start with the given system of linear equations: \[ \left\{ \begin{aligned} 3x - 8y & = 99 \\ 4y & = -32x - 16 \end{aligned} \right. \]

Step 2: Rearrange the Second Equation

We rearrange the second equation to express \(y\) in terms of \(x\): \[ 4y = -32x - 16 \implies y = -8x - 4 \]

Step 3: Substitute \(y\) in the First Equation

Next, we substitute \(y = -8x - 4\) into the first equation: \[ 3x - 8(-8x - 4) = 99 \]

Step 4: Simplify the Equation

We simplify the equation: \[ 3x + 64x + 32 = 99 \implies 67x + 32 = 99 \]

Step 5: Solve for \(x\)

Now, we isolate \(x\): \[ 67x = 99 - 32 \implies 67x = 67 \implies x = 1 \]

Step 6: Substitute \(x\) Back to Find \(y\)

We substitute \(x = 1\) back into the equation for \(y\): \[ y = -8(1) - 4 = -8 - 4 = -12 \]

Step 7: State the Solution

The solution to the system of equations is: \[ x = 1, \quad y = -12 \]

Final Answer

\[ x = \boxed{1}, \quad y = \boxed{-12} \]

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