Hi! My teacher wanted me to sketch the graph of solution set of each system. For the first question, she wants me to use the slope intercept form and the second question using a table of values, but, I'm a little lost. Can someone help? Thanks!
1.) 3x + 2y < 6
x > 0
y > 0
2.) 2x2 + y ≥ 2
x ≤ 2
y ≤ 1
We cannot graph on these posts.
Of course! I'd be happy to help you solve these questions.
1.) For the first question, you need to sketch the graph of the solution set for the given system using the slope-intercept form. To do this, you can follow these steps:
Step 1: Solve each inequality for y in terms of x to convert them into slope-intercept form (y = mx + b). Let's start with the first inequality: 3x + 2y < 6. Rearranging this inequality, we get:
2y < 6 - 3x
y < (6 - 3x) / 2
Step 2: Now, let's focus on the second inequality: x > 0. Since this inequality is already in terms of x, we don't need to rearrange anything.
Step 3: Similarly, the third inequality y > 0 is already in terms of y, so there is no rearranging needed.
Step 4: Plot the graph of the equality part for each inequality on a Cartesian coordinate system. It is important to note that inequalities involving < or > will be plotted with dotted lines since they don't include the boundary, unlike ≤ or ≥.
Step 5: Shade the area below the line for y < (6 - 3x) / 2, to represent y being less than the value given by the equation.
Step 6: Shade the area to the right of the x-axis to represent x > 0 since the graph is restricted to the positive x-axis.
Step 7: Shade the area above the x-axis to represent y > 0 since the graph is restricted to the positive y-axis.
Combining these shaded regions, you'll have the graph of the solution set for the given system.
2.) For the second question, you need to sketch the graph of the solution set using a table of values. Here's how you can do that:
Step 1: Write down the given inequalities: 2x^2 + y ≥ 2, x ≤ 2, and y ≤ 1.
Step 2: Create a table to map out the values of x and y for the given inequalities. Start by choosing some values for x, such as -2, -1, 0, 1, and 2. Substitute these values into each inequality and solve for y.
Step 3: Once you have a few points, plot them on a Cartesian coordinate system.
Step 4: Connect the points on the graph using a smooth curve for the inequality 2x^2 + y ≥ 2. Since this inequality includes the boundary (≥), the line connecting the points should be solid.
Step 5: Shade the area above the line to represent the region where 2x^2 + y is greater than or equal to 2.
Step 6: Shade the area to the left of the line x = 2 to represent the region where x is less than or equal to 2.
Step 7: Shade the area below the line y = 1 to represent the region where y is less than or equal to 1.
Combining these shaded regions, you'll have the graph of the solution set for the given system.
I hope these explanations help you with your sketches! Let me know if you have any further questions.