You have another system of linear equations:

\[
y = 7.8663x - 9.618
\]
\[
y = 4.19357x + 1.4645
\]

To find the point of intersection, set the two equations equal to each other:

\[
7.8663x - 9.618 = 4.19357x + 1.4645
\]

Next, solve for \(x\):

\[
7.8663x - 4.19357x = 1.4645 + 9.618
\]

\[
3.67273x = 11.0825
\]

\[
x = \frac{11.0825}{3.67273} \approx 3.0185
\]

Now, substitute \(x = 3.0185\) back into either of the original equations to find the corresponding \(y\)-value. Let's use the first equation:

\[
y = 7.8663(3.0185) - 9.618 \approx 23.7353 - 9.618 \approx 14.1173
\]

Thus, the solution to the system of equations is approximately:

\[
(x, y) \approx (3.0185, 14.1173)
\]

Would you like more details or have any questions?

Here are 5 related questions you might explore:
1. How do you verify the solution to a system of linear equations?
2. What are the implications of the slopes of two lines when solving a system of equations?
3. Can you solve systems of equations with more than two variables?
4. How can you use graphing to check the solution of a system of linear equations?
5. What happens if two linear equations represent parallel lines?

**Tip:** When solving systems of equations, graphing can provide a visual check of your algebraic solution, especially when the equations are more complex.

Learn how to find the intersection point of two linear equations y = 7.8663*x - 9.618 and y = 4.19357*x + 1.4645. This problem involves solving a system of linear equations using substitution and verification methods. Suitable for students in Grades 9-12.

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