Math Problem Statement

What is the solution to this linear system? Enter a value in each box to create an ordered pair.

Solution

The graph in the image shows the intersection of two lines, which represent the solution to the linear system. The solution to a system of linear equations graphically is the point where the two lines intersect.

From the graph, it appears that the two lines intersect at the point (2,2)(-2, 2). This is the solution to the system of equations, meaning the ordered pair that satisfies both equations.

So, the solution is: (2,2)(-2, 2)

Would you like more details or have any further questions?

Here are some related questions to deepen your understanding:

  1. What is the meaning of a linear system in algebra?
  2. How can we algebraically solve a system of two linear equations?
  3. What does it mean when two lines intersect, are parallel, or coincide in terms of solutions?
  4. Can you describe the graphical meaning of a system with no solutions?
  5. How can we verify the solution (2,2)(-2, 2) using the equations of the lines?

Tip: Always check if the point of intersection lies on both lines by substituting the coordinates into the original equations.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Graphing Systems of Equations

Formulas

None (graphical solution)

Theorems

Intersection Theorem: The point where two lines intersect is the solution to the system of equations.

Suitable Grade Level

Grades 7-9