The Real Number Line. The most intuitive way is to use the real number line.
Introduction We use inequalities when there is a range of possible answers for a situation. We can explore the possibilities of an inequality using a number line. This is sufficient in simple situations, such as inequalities with just one variable. In these cases, we use linear inequalities —inequalities that can be written in the form of a linear equation.
In this inequality, the boundary line is plotted as a dashed line. Notice that the two examples above used the variables x and y.
It is standard practice to use these variables when you are graphing an inequality on a x, y coordinate grid. We could have represented both of these relationships on a number line, and depending on the problem we were trying to solve, it may have been easier to do so. Things get a little more interesting, though, when we plot linear inequalities with two variables.
Take a look at the three points that have been identified on the graph. Do you see that the points in the boundary region have x values greater than the y values, while the point outside this region do not?solve each system graphically. be sure to check your solution. if a system has an infinite number of solutions, use the set-builder notation to write solution set.
if a system has no solution, state this. where appropriate, round to the nearest hundredth.
For example, x 2 0 has no solutions if the domain is the real numbers.. x 5 has only one solution (= 4) if the domain consists of the squares of positive even numbers.. x 5 has infinitely many solutions if the domain is the rational numbers or real numbers. If the graphs of the equations are parallel, then the system of equations will have no solution.
Because parallel lines never intersect each other. Because parallel lines never intersect each other.
If the system has at least one solution (one solution or infinitely many solutions), then it is said to be consistent system. Mathematics: Inequalities in One and Two Variables Finite solution sets in inequalities 5. Solution sets in inequalities with upper and lower bounds 6.
Some applications of one-variable inequalities 7. Solving two-variable inequalities A mathematician would write this problem as an inequality. A system of equations is called an inconsistent system of equations if there is no solution because the lines are parallel.
A dependent system of equations is when the same line is written in two different forms so that there are infinite solutions. The system has no solution if the lines are parallel.
If they are the same line, they have infinitely many points in common so the system has infinitely many solutions. If the lines intersect, that one point where they cross represents the one pair of numbers that satisfies both equations.