y<=1/4x+2 and y>1/2x+3 find solution to the simultaneous inequalities

Answer 1

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.