Andymath.com features free videos, notes, and practice problems with answers! Printable pages make math easy. Are you ready to be a mathmagician?
Graph each system of inequalities.
\(\textbf{1)}\) \( y\lt-3x+2 \)
\(\) \( y\ge\frac{1}{2}x-1 \)
\(\textbf{2)}\) \( y\gt x \)
\(\) \( y\lt2x \)
\(\textbf{3)}\) \( x+2y\le10 \)
\(\) \( 2x-y\le4 \)
\(\textbf{4)}\) \( x\le4 \)
\(\) \( x\ge-2 \)
\(\textbf{5)}\) \( y\lt5 \)
\(\) \( x\gt-2 \)
\(\textbf{6)}\) \( y\lt8 \)
\(\) \( y\gt2 \)
\(\textbf{7)}\) \( y\gt x^2 \)
\(\) \( y\lt4 \)
\(\textbf{8)}\) \( x^2+y^2\le36 \)
\(\) \( y\ge3 \)
\(\textbf{9)}\) \( y\ge x^2-4 \)
\(\) \( y\le -x^2+6 \)
\(\textbf{10)}\) \( y\le x^2+3 \)
\(\) \( y\ge x^2-5 \)
See Related Pages\(\)
\(\bullet\text{ Solving Systems with Substitution}\)
\(\,\,\,\,\,\,\,\,y=−2x+5\)
\(\,\,\,\,\,\,\,\,y=x-1…\)
\(\bullet\text{ Solving Systems with Elimination}\)
\(\,\,\,\,\,\,\,\,7x+4y=31 \)
\(\,\,\,\,\,\,\,\,3x+2y=15…\)
\(\bullet\text{ 3 variable systems}\)
\(\,\,\,\,\,\,\,\,2x+3y−5z=−7 \)
\(\,\,\,\,\,\,\,\,3x−6y+4z=3 \)
\(\,\,\,\,\,\,\,\,x+4y+2z=15…\)
\(\bullet\text{ Nonlinear Systems}\)
\(\,\,\,\,\,\,\,\,x^2+y^2=8 \)
\(\,\,\,\,\,\,\,\,y=x…\)
Desmos Graphing Tool
\( \text{Click Here for Helpful Desmos Graph}\)
In Summary
Graphing systems of inequalities involves plotting the solutions to multiple inequalities on the same coordinate plane. The solution region is the area where all are true.
Graphing systems of inequalities is typically covered in a high school or college algebra or pre-calculus class.
Graphing systems of inequalities is the method used to represent and solve real-world problems involving constraints or limitations, such as finding the maximum or minimum value of a quantity subject to certain conditions. A real world example example is in finding the maximum profit that can be earned subject to a given a set of production and market conditions.
About Andymath.com
Andymath.com is a free math website with the mission of helping students, teachers and tutors find helpful notes, useful sample problems with answers including step by step solutions, and other related materials to supplement classroom learning. If you have any requests for additional content, please contact Andy at tutoring@andymath.com. He will promptly add the content.
Topics cover Elementary Math, Middle School, Algebra, Geometry, Algebra 2/Pre-calculus/Trig, Calculus and Probability/Statistics. In the future, I hope to add Physics and Linear Algebra content.
Visit me on Youtube, Tiktok, Instagram and Facebook. Andymath content has a unique approach to presenting mathematics. The clear explanations, strong visuals mixed with dry humor regularly get millions of views. We are open to collaborations of all types, please contact Andy at tutoring@andymath.com for all enquiries. To offer financial support, visit my Patreon page. Let’s help students understand the math way of thinking!
Thank you for visiting. How exciting!