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y<=1/4x+2 and y>1/2x+3 find solution to the simultaneous inequalities
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GPT 3.5
To find the solution to the simultaneous inequalities, we need to find the values of x and y that satisfy both inequalities.
First, let's graph the first inequality, y <= 1/4x + 2:
- Start by graphing the line y = 1/4x + 2. To graph this line, plot two points, like (0, 2) and (4, 3), then draw a straight line through them.
Next, shade the region below the line, since y is less than or equal to 1/4x + 2.
Now, let's graph the second inequality, y > 1/2x + 3:
- Start by graphing the line y = 1/2x + 3. To graph this line, plot two points, like (0, 3) and (4, 5), then draw a straight line through them.
Next, shade the region above the line, since y is greater than 1/2x + 3.
The solution to the simultaneous inequalities is the region that satisfies both inequalities, which is the shaded region that is below the line y = 1/4x + 2 and above the line y = 1/2x + 3.
First, let's graph the first inequality, y <= 1/4x + 2:
- Start by graphing the line y = 1/4x + 2. To graph this line, plot two points, like (0, 2) and (4, 3), then draw a straight line through them.
Next, shade the region below the line, since y is less than or equal to 1/4x + 2.
Now, let's graph the second inequality, y > 1/2x + 3:
- Start by graphing the line y = 1/2x + 3. To graph this line, plot two points, like (0, 3) and (4, 5), then draw a straight line through them.
Next, shade the region above the line, since y is greater than 1/2x + 3.
The solution to the simultaneous inequalities is the region that satisfies both inequalities, which is the shaded region that is below the line y = 1/4x + 2 and above the line y = 1/2x + 3.
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