Math Problem Statement

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) (Give coordinates)

Solution

To determine the values of xx and yy that satisfy both equations graphically, let's analyze the system of equations:

  1. y=2x23x4y = 2x^2 - 3x - 4
  2. y=24xy = 2 - 4x

Solution Outline

  1. We will graph both equations within the specified range for xx (from x=3x = -3 to x=3x = 3).
  2. The intersection points of the two graphs represent the (x,y)(x, y) coordinates that simultaneously satisfy both equations.

Let's plot these functions.

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Math Problem Analysis

Mathematical Concepts

Algebra
Graphing Functions
Systems of Equations

Formulas

Quadratic equation: y = ax² + bx + c
Linear equation: y = mx + b

Theorems

Intersection of functions represents solutions to simultaneous equations

Suitable Grade Level

Grades 9-11