BUT DO NOT forget to replace the equal symbol with the original inequality symbol at the END of the problem! In doing so, you can treat the inequality like an equation.
#Solutions of equations and inequalities equation systems how to
How To Solve Systems of Inequalities Graphicallyġ) Write the inequality in slope-intercept form or in the form \(y = mx + b\).įor example, if asked to solve \(x + y \leq 10\), we first re-write as \(y \leq -x + 10\).Ģ) Temporarily exchange the given inequality symbol (in this case \(\leq\)) for just equal symbol. In light of this fact, it may be easiest to find a solution set for inequalities by solving the system graphically. There are endless solutions for inequalities. Usually this is written as = on computers because it is easier to type. The symbol \(\leq\) means less than or equal to.Since it is a solid line, the inequality is y ≤ - x + 6.Solving Systems of Inequalities We first need to review the symbols for inequalities: The shaded area is to the left (or below) the line. Our second inequality is y ≥ 2.įinally, we'll take the diagonal line of y = - x + 6. Next we'll take the region above (and including) the horizontal line y = 2. That means our first inequality is x ≥ 1. This clearly is the to the right and including the vertical line at x = 1. Write a system of inequalities that has this solution (the triangle in the middle): Notice we used the equal sign here because we are talking about the boundary. The boundary of the solution are the equations: The solution is the intersection of the two shaded regions (the dark green region). Merging them together to find the overlap, we get:
We'll use the same method as before and try to first solve for y for each equation. The key here is that we need to think of each graph and find the intersection or overlap and that will be our solution. Solve the system of inequalities and state the boundary. Yes! The point (0, 0) lies within the solution. How about (0, 0)? That clearly lies in the purple shading but let's check algebraically by substituting 0 in for x and y to make sure it satisfies the inequality. We must find a point within our solution of the inequality.
No coloring outside of the lines! If you do, "No soup for you." Then, we can shade above since our solution is greater than. Since we have a >, we need a dotted line for our parabola because the solution cannot be anywhere on that curve. To make things easier, we need to solve first for y (by subtracting 3 from each side). If it is 2 x 2, state it's boundary and find a point that lies in the solution to the inequality. If you have the ≤ sign, you need to draw a solid line.Then you will go down 3, and to the right 1 to apply your slope. Go up 5 on the y-axis and make your point for the y-intercept. Pretend it is an equal sign and graph like you would a normal linear equation (remember y = mx + b).Hey! Guess what? It's already solved for y. Try, try, try if you can to solve for y.Suggestions for graphing this inequality are We'll show you graphical solutions and find out if specific points lie in solution the solution sets.įirst, lets take a walk down memory lane and revisit what an inequality is. We learned about where lines and planes intersect in the last section, but this section we want to know about where inequalities intersect. It's all about where regions of area overlap. The on-the-job training in this section will be learning how to graph and solve systems of inequalities. There will be no overlap in benefits, and you feel unequal to your peers! Sounds like a terrible job, but we would like to take you on a little job training. You will get less than or equal to your fair share. Can you draw a picture and shade it in? If so, you qualify for the position "Systems of Inequalities Solver." The benefits are so-so.
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