Question
Which two quadrants contain all the solution of the following system why is greater than 4x - 2 Y is greater than -3x + 5
Answers
GPT 3.5
To determine which quadrants contain all the solutions of the system, we need to analyze the inequalities separately.
The first inequality is "y > 4x - 2". To graph this inequality, we can start by graphing the line "y = 4x - 2" (which is a straight line with a slope of 4 and y-intercept of -2). Since it is a "greater than" inequality, we want to shade the area above the line.
The second inequality is "y > -3x + 5". To graph this inequality, we can plot the line "y = -3x + 5" (which is a straight line with a slope of -3 and y-intercept of 5). Again, since it is a "greater than" inequality, we want to shade the area above the line.
Now, let's find the two quadrants that contain all the solutions:
1. Quadrants I and II: Since the inequalities are both "greater than" inequalities, we want to shade both areas above the lines. Quadrants I and II are above the x-axis, which means any points in these quadrants would satisfy both inequalities simultaneously.
Therefore, the two quadrants that contain all the solutions are Quadrants I and II.
The first inequality is "y > 4x - 2". To graph this inequality, we can start by graphing the line "y = 4x - 2" (which is a straight line with a slope of 4 and y-intercept of -2). Since it is a "greater than" inequality, we want to shade the area above the line.
The second inequality is "y > -3x + 5". To graph this inequality, we can plot the line "y = -3x + 5" (which is a straight line with a slope of -3 and y-intercept of 5). Again, since it is a "greater than" inequality, we want to shade the area above the line.
Now, let's find the two quadrants that contain all the solutions:
1. Quadrants I and II: Since the inequalities are both "greater than" inequalities, we want to shade both areas above the lines. Quadrants I and II are above the x-axis, which means any points in these quadrants would satisfy both inequalities simultaneously.
Therefore, the two quadrants that contain all the solutions are Quadrants I and II.