solve the system of two linear inequalities graphically. 7x+8y<56. x>3. find the region with points that satisfy both inequalities select the region you wish to be shaded A,b,c or d
To solve the system of two linear inequalities graphically, we will graph each inequality separately and then shade in the region that satisfies both inequalities.
First, let's graph the inequality 7x + 8y < 56.
To graph this inequality, we will start by graphing the equation 7x + 8y = 56, which is the boundary line of the inequality.
To find the x-intercept, set y = 0 and solve for x:
7x + 8(0) = 56
7x = 56
x = 8
So the x-intercept of the line is (8, 0).
To find the y-intercept, set x = 0 and solve for y:
7(0) + 8y = 56
8y = 56
y = 7
So the y-intercept of the line is (0, 7).
Plot these two intercept points and draw a straight line passing through them.
Next, we need to determine which side of the line to shade. Since the inequality is less than (<), we need to shade the region below the line.
Now, let's graph the inequality x > 3.
To graph this inequality, we will draw a dashed vertical line at x = 3, since x is greater than 3.
To determine which side of the line to shade, we know that x is greater than 3, so we need to shade the region to the right of the dashed line.
Now, we need to find the region that satisfies both inequalities.
Since we want to shade the region that satisfies both inequalities, we need to shade the region that is below the line in the first inequality and to the right of the dashed line in the second inequality.
The shaded region should be C.
I hope this helps! Let me know if you have any further questions.