Math Problem Statement

Which of the following represents the solution to a system of linear equations on graphs? Responses

The slopes of the lines. The slopes of the lines.

The x-intercepts of the lines. The x-intercepts of the lines.

The y-intersects of the lines. The y-intersects of the lines.

The point at which the lines intersect.

Solution

The correct answer is:

The point at which the lines intersect.

In a system of linear equations, the solution is represented by the point where the two lines intersect on the graph. This point gives the values of xx and yy that satisfy both equations simultaneously.

Would you like any further details on this topic or how to solve systems graphically?

Here are some follow-up questions:

  1. How do you graphically solve a system of linear equations?
  2. What does it mean if two lines never intersect on a graph?
  3. How do you determine the slope and y-intercept of a line from an equation?
  4. What are the different types of solutions a system of linear equations can have (one solution, no solution, infinitely many)?
  5. How do you check your solution after graphing the system?

Tip: When graphing two linear equations, always make sure to label the axes and plot the lines accurately to ensure the intersection point is correct.

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Math Problem Analysis

Mathematical Concepts

Algebra
Systems of Linear Equations
Graphing

Formulas

Slope-intercept form: y = mx + b
Point of intersection of two lines

Theorems

Two lines intersect at a single point if they have different slopes
Parallel lines have no solution
Coincident lines have infinitely many solutions

Suitable Grade Level

Grades 8-10