Question

Найди точку пересечения графиков, заданных формулами 10x+2y=87 и y=−2,5x без построения.

Answer 1

10x+2y=87 и y=−2,5x
подставляем в первое уравнение вместо у -2,5х

10х-5х=87
5х=87
х=17,4

у=-2,5*17,4=-43,5

Answer 2

I can help you with your math problem. To find the point of intersection of the graphs given by the formulas $10x+2y=87$ and $y=-2.5x$, you need to solve the system of equations:

$$ \begin{cases} 10x+2y=87\\ y=-2.5x \end{cases} $$

You can do this by substituting the second equation into the first one and solving for $x$:

$$ 10x+2(-2.5x)=87\\ 10x-5x=87\\ 5x=87\\ x=\frac{87}{5} $$

Then, you can plug in the value of $x$ into either equation and solve for $y$:

$$ y=-2.5\left(\frac{87}{5}\right)\\ y=-43.5 $$

Therefore, the point of intersection is $\left(\frac{87}{5},-43.5\right)$. You can check your answer by plugging in the coordinates into both equations and verifying that they are true.

If you want to see the graphs of the equations, you can use this [online calculator](https://www.desmos.com/calculator/dxvt1xgqsz?lang=ru). You can also find more examples of how to find the points of intersection of graphs [here](https://spravochnick.ru/matematika/kak_nayti_koordinaty_tochek_peresecheniya_grafika_funkcii_primery_resheniya/) and [here](https://ru.wikihow.com/%D0%BD%D0%B0%D0%B9%D1%82%D0%B8-%D1%82%D0%BE%D1%87%D0%BA%D1%83-%D0%BF%D0%B5%D1%80%D0%B5%D1%81%D0%B5%D1%87%D0%B5%D0%BD%D0%B8%D1%8F-%D1%81-%D0%BE%D1%81%D1%8C%D1%8E-%D0%A5). I hope this helps.