Question

4(2x-y+3)-3 (x-2y+3)=48 3(3x-4y+3)+4(4x-2y-9)=48

Answer 1

Ответ:

4(2x-y+3)-3 (x-2y+3)=48= dу/dx= -5/2

3(3x-4y+3)+4(4x-2y-9)=48= dу/dx= 5/4

Объяснение:

Answer 2

To solve the system of linear equations with two variables, we can use the elimination method. Here are the steps:

- First, we need to simplify each equation by distributing and combining like terms. For the first equation, we have:

$$4(2x-y+3)-3+(x-2y+3)=48$$ $$\Rightarrow 8x-4y+12-3+x-2y+3=48$$ $$\Rightarrow 9x-6y+12=48$$

For the second equation, we have:

$$3(3x-4y+3)+4(4x-2y-9)=48$$ $$\Rightarrow 9x-12y+9+16x-8y-36=48$$ $$\Rightarrow 25x-20y-27=48$$

- Next, we need to multiply one or both equations by a constant so that the coefficients of one variable are opposites. In this case, we can multiply the first equation by 5 and the second equation by 3 to get:

$$45x-30y+60=240$$ $$75x-60y-81=144$$

- Then, we need to add the two equations to eliminate one variable. In this case, we can eliminate y by adding the equations:

$$45x-30y+60=240$$ $$+$$ $$75x-60y-81=144$$ $$\Rightarrow 120x-90y-21=384$$ $$\Rightarrow 120x-21=384$$

- Next, we need to solve for the remaining variable. In this case, we can solve for x by dividing both sides by 120:

$$120x-21=384$$ $$\Rightarrow 120x=384+21$$ $$\Rightarrow 120x=405$$ $$\Rightarrow x=\frac{405}{120}$$ $$\Rightarrow x=\frac{27}{8}$$

- Finally, we need to substitute the value of x into either of the original equations to find the value of y. In this case, we can use the first equation:

$$9x-6y+12=48$$ $$\Rightarrow 9\left(\frac{27}{8}\right)-6y+12=48$$ $$\Rightarrow \frac{243}{8}-6y+12=48$$ $$\Rightarrow -6y=\frac{384-243-96}{8}$$ $$\Rightarrow -6y=-27$$ $$\Rightarrow y=\frac{27}{6}$$ $$\Rightarrow y=\frac{9}{2}$$

Therefore, the solution of the system of linear equations is $$\left(\frac{27}{8},\frac{9}{2}\right)$$.

You can check the solution by plugging in the values of x and y into both equations and verifying that they are true. You can also use the graphical method to see the intersection point of the two lines, which is the solution of the system. You can watch some videos on how to solve systems of linear equations by different methods from the video results . You can also read some web pages on the topic from the web search results . You can also use the question answering results to get a quick answer to a specific question. I hope this helps you understand how to solve linear equations with two variables.solve linear equations with two variables