You have a system of two linear equations:

\[
y = -7.3177x - 8.65
\]
\[
y = 3.926x + 1.4984
\]

To find the solution (i.e., the point where these two lines intersect), we can set the two equations equal to each other since both are equal to \(y\):

\[
-7.3177x - 8.65 = 3.926x + 1.4984
\]

Next, let's solve for \(x\):

\[
-7.3177x - 3.926x = 1.4984 + 8.65
\]

\[
-11.2437x = 10.1484
\]

\[
x = \frac{10.1484}{-11.2437} \approx -0.9026
\]

Now, substitute \(x = -0.9026\) back into either of the original equations to find the corresponding \(y\)-value. Let's use the second equation:

\[
y = 3.926(-0.9026) + 1.4984 \approx -3.5429 + 1.4984 \approx -2.0445
\]

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

\[
(x, y) \approx (-0.9026, -2.0445)
\]

Would you like more details or have any questions?

Here are 5 related questions you might explore:
1. How do you interpret the solution of a system of linear equations geometrically?
2. What does it mean if the slopes of the two lines are equal in a system of linear equations?
3. Can you solve a system of equations using matrix methods like Gaussian elimination?
4. How do different methods (substitution, elimination, graphing) compare when solving systems of linear equations?
5. What is the significance of the y-intercept in a linear equation?

**Tip:** When dealing with linear equations, always double-check the signs and operations, as small errors can lead to incorrect solutions.

Learn how to solve a system of linear equations involving -7.3177x - 8.65 = 3.926x + 1.4984. Follow a step-by-step solution method to find the intersection point of two linear equations. Suitable for Grades 7-9.

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