Determine graphically the values of x and y which simultaneously satisfy the equation 
( y =2 × x² -3x - 4)and (y = 2 - 4x)
Use range of x from (x = -3) to (x =3)


To solve this graphically, we need to plot the two equations:

1. \( y = 2x^2 - 3x - 4 \) (a quadratic equation that will form a parabola)
2. \( y = 2 - 4x \) (a linear equation forming a straight line)

### Steps:
1. **Define the Range for \( x \)**: We'll plot \( x \) values from \( -3 \) to \( 3 \).
2. **Plot Both Equations**: We'll graph each equation within this range.
3. **Find Intersection Points**: The points where the two graphs intersect will provide the values of \( x \) and \( y \) that satisfy both equations.

Let's plot it.It seems like I can’t do more advanced data analysis right now. Please try again later. 

However, here’s a suggestion on how you could solve this graphically yourself:

1. Plot both equations within the range of \( x \) from \(-3\) to \(3\).
2. For the quadratic equation \( y = 2x^2 - 3x - 4 \), create a set of points for \( x \) in the range and calculate corresponding \( y \)-values.
3. Similarly, for the linear equation \( y = 2 - 4x \), calculate \( y \)-values for the same \( x \)-range.
4. Draw both graphs on the same axes, and identify the intersection points where both equations give the same \( y \)-value for the same \( x \)-value. These points will be your solutions.

Would you like a more detailed step-by-step on how to do this manually or any additional assistance with another part of the problem?

### Here are some related questions you might be interested in:
1. How can I determine intersections between two functions algebraically?
2. How can I interpret intersections on a graph to find solutions?
3. What role does the quadratic shape play in graphical solutions?
4. How does changing the range of \( x \) affect the graph and solutions?
5. How can we confirm the solutions we find graphically?

**Tip:** When plotting manually, check multiple values for accuracy, especially near where curves intersect.

Determine graphically the values of x and y which simultaneously satisfy the equation (y = 2x² - 3x - 4) and (y = 2 - 4x). Use range of x from (x = -3) to (x = 3).

Learn how to graphically determine the values of x and y that satisfy both y = 2x² - 3x - 4 and y = 2 - 4x, using x-values from -3 to 3. Explore the intersection points of a quadratic and a linear function to find solutions visually. Ideal for students in Grades 9-11 studying algebra and graphical solutions.

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