Math Problem Statement

What is the solution to the system of equations graphed below? y = -2x - 3 y = 3x + 2

Solution

The question asks for the solution to the system of equations y=2x3y = -2x - 3 and y=3x+2y = 3x + 2, based on the graph. The solution is the point where the two lines intersect.

From the graph, the two lines intersect at the point (1,1)(-1, -1). Therefore, the solution to the system of equations is:

Answer: A. (-1, -1)

Would you like a detailed explanation of how this is solved algebraically or any further clarification?


Here are 5 related questions for further exploration:

  1. How do you solve a system of equations algebraically using substitution?
  2. How do you determine the slope and y-intercept from an equation in slope-intercept form?
  3. What does it mean when two lines do not intersect on a graph?
  4. How can you check if a point is a solution to a system of equations?
  5. How do parallel and perpendicular lines behave in a system of equations?

Tip: Always double-check the intersection point by substituting its coordinates into both equations!

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Algebra
Graphing Systems of Equations
Slope-Intercept Form

Formulas

Slope-intercept form: y = mx + b

Theorems

Intersection of two lines on a graph represents the solution to the system

Suitable Grade Level

Grades 8-10