System Of Linear Equations

Concept: Each equation represents a line. We need to identify these lines and the shape they form. Step 1: Identify the four lines
From first system: (Vertical line) (Horizontal line)
From second system: (Vertical line) (Horizontal line) Step 2: Visualize or sketch the lines These four lines are . Vertical lines pass through and . Horizontal lines pass through and . Step 3: Determine the properties of the enclosed shape The lines form a quadrilateral.
The horizontal sides are bounded by and . The length of these sides is units.
The vertical sides are bounded by and . The length of these sides is units. Since horizontal lines are perpendicular to vertical lines, all angles of the enclosed quadrilateral are . The lengths of all four sides are equal (9 units). A quadrilateral with four right angles and four equal sides is a square. Step 4: Conclusion The lines enclose a square region. "Square region" is the most specific correct description. (A square is also a rectangle, but "square" is more precise). The circled option (3) "A triangular region" in the original image is incorrect as four lines typically form a quadrilateral.