https://file.aiquickdraw.com/mathbot/file/1726251479770k5p5bctn.jpg

Solve the system of equations graphed on the coordinate axes below.

y, equals, minus, 2, x

*y*=

−2*x*

y, equals, start fraction, 4, divided by, 3, end fraction, x

*y*=

34​*x*

The image presents a system of two linear equations, graphed on the coordinate plane:

1. \( y = -2x \)
2. \( y = \frac{4}{3}x \)

These equations represent straight lines, and their solution corresponds to the point where the two lines intersect.

### Steps to Solve the System:

To find the point of intersection, we can set the two equations equal to each other since both are equal to \( y \):

\[
-2x = \frac{4}{3}x
\]

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

\[
-2x = \frac{4}{3}x
\]

First, eliminate the fraction by multiplying both sides of the equation by 3:

\[
3(-2x) = 4x
\]
\[
-6x = 4x
\]

Next, move all terms involving \( x \) to one side:

\[
-6x - 4x = 0
\]
\[
-10x = 0
\]

Now, divide by \(-10\):

\[
x = 0
\]

### Finding \( y \):

Substitute \( x = 0 \) into either of the original equations. Using the first equation:

\[
y = -2(0) = 0
\]

Thus, the solution to the system is:

\[
(x, y) = (0, 0)
\]

The lines intersect at the origin, \( (0, 0) \).

---

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:
1. How do we determine the slope of a line from its equation?
2. What does it mean geometrically when two lines intersect at a point?
3. What happens if two lines have the same slope but different y-intercepts?
4. Can systems of linear equations have no solution? Why?
5. What is the graphical representation of parallel lines on a coordinate plane?

**Tip:** When solving systems of equations graphically, the solution is the point where the lines intersect. If no intersection exists, the system has no solution or infinitely many solutions (if the lines coincide).

Solve the system of equations graphed on the coordinate axes below: y = -2x and y = (4/3)x.

Learn how to solve the system of linear equations y = -2x and y = (4/3)x, by finding the point of intersection. Understand the steps for solving systems graphically, including key algebraic concepts. Suitable for students in Grades 8-10.

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