https://file.aiquickdraw.com/mathbot/file/1726397525519cd6m3w5e.jpg

The task in the image asks to "Знайдіть координати точки перетину прямих" (Find the coordinates of the intersection point of the lines). The two equations provided are:

1. \( x - 8y + 7 = 0 \)
2. \( 0.12x - 4y - 3 = 0 \)

To find the intersection point, we can solve these two linear equations simultaneously. Let's proceed by solving this system step by step.

### Equation 1:
\[
x - 8y + 7 = 0 \quad \text{(which simplifies to)} \quad x = 8y - 7
\]

### Equation 2:
\[
0.12x - 4y - 3 = 0 \quad \text{(which simplifies to)} \quad x = \frac{4y + 3}{0.12}
\]

I will now solve this system to find the coordinates of the intersection point.The coordinates of the intersection point of the given lines are approximately \( x \approx -17.11 \) and \( y \approx -1.26 \).

Would you like a detailed explanation of the solving process, or do you have any questions?

Here are five related questions to explore further:
1. How do we solve linear equations using substitution?
2. Can you solve systems of linear equations graphically?
3. What are the possible types of solutions for systems of two linear equations?
4. How does the slope of the lines affect the intersection point?
5. How can we apply these methods to more complex systems of equations?

**Tip:** When solving systems of equations, using substitution or elimination methods can simplify the problem, especially when equations are given in different forms.

Знайдіть координати точки перетину прямих: x - 8y + 7 = 0; 0.12x - 4y - 3 = 0.

Learn how to find the coordinates of the intersection point of the two linear equations: x - 8y + 7 = 0 and 0.12x - 4y - 3 = 0. This guide includes a step-by-step explanation using substitution and equation simplification, suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation