pleas help me to solve this[tex]x - 2y \leqslant - 2[/tex]and[tex]y \geqslant x + 2[/tex]
Answer (1)
Step-by-step explanation:x - 2y ≤ -2: This inequality represents a line with a slope of 1/2 (because the coefficient of x is 1 and the coefficient of y is -2). The "less than or equal to" sign means we're looking for the area below (or on) this line.y ≥ x + 2: This inequality represents a line with a slope of 1 (because the coefficient of x is 1 and the coefficient of y is 1). The "greater than or equal to" sign means we're looking for the area above (or on) this line.Solving the SystemGraph the Lines: Start by graphing both lines on the same coordinate plane.x - 2y = -2: To graph this, find the x and y intercepts:When x = 0, y = 1When y = 0, x = -2y = x + 2: To graph this, find the y-intercept (2) and use the slope of 1 (rise 1, run 1) to find another point.Shade the Solution Area: The solution to the system of inequalities is the area where the shaded regions of both inequalities overlap.x - 2y ≤ -2: Shade the area below the line.y ≥ x + 2: Shade the area above the line.Identify the Overlap: The overlapping shaded area represents the set of all points (x, y) that satisfy both inequalities.Let me know if you'd like me to help you graph these lines or if you have any other questions!
