Question

3x+12y=0,75 8x+8y=1 Система управления

Answer 1

Ответ: (1/12;1/24)

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Answer 2

It appears that you have provided two linear equations:

1. $3x + 12y = 0.75$
2. $8x + 8y = 1$

To solve this system of equations, we can use one of the following methods:

1. Substitution Method:

   • From equation (1), we can express $x$ in terms of $y$ as follows: $3x = 0.75 - 12y \Rightarrow x = 0.25 - 4y$
   • Substitute this expression for $x$ into equation (2): $8(0.25 - 4y) + 8y = 1$
   • Simplify and solve for $y$: $2 - 32y + 8y = 1 \Rightarrow -24y = -1 \Rightarrow y = \frac{1}{24}$
   • Now, substitute the value of $y$ back into either equation (1) or (2) to solve for $x$: $3x + 12\left(\frac{1}{24}\right) = 0.75 \Rightarrow 3x + 0.5 = 0.75 \Rightarrow 3x = 0.25 \Rightarrow x = \frac{1}{12}$

   So, the solution to the system of equations is $x = \frac{1}{12}$ and $y = \frac{1}{24}$.

2. Elimination Method:

   • Multiply both equations by suitable constants to make the coefficients of $y$ in both equations equal. In this case, we can multiply the first equation by 2 and the second equation by -3 to eliminate $y$.
   • The modified equations become: $6x + 24y = 1.5$ and $-24x - 24y = -3$
   • Now, add the two equations to eliminate $y$: $6x - 24x + 24y - 24y = 1.5 - 3$
   • Simplify and solve for $x$: $-18x = -1.5 \Rightarrow x = \frac{1}{12}$
   • Substitute the value of $x$ back into either equation (1) or (2) to solve for $y$: $3\left(\frac{1}{12}\right) + 12y = 0.75 \Rightarrow \frac{1}{4} + 12y = 0.75 \Rightarrow 12y = 0.75 - \frac{1}{4} \Rightarrow y = \frac{1}{24}$

   So, the solution to the system of equations is $x = \frac{1}{12}$ and $y = \frac{1}{24}$.

Both methods yield the same solution for the system of equations: $x = \frac{1}{12}$ and $y = \frac{1}{24}$.