0
The solutions to a linear inequality are the points in the plane that make the inequality true?
Yes, and no.
The solution set to an inequality are those points which satisfy the inequality.
A linear inequality is one in which no variable has a power greater than 1. Only if there are two variables will the solution be points in a plane; if there are more than two variables then the solution set will be points in a higher space, for example the solution set to the linear inequality x + y + z < 1 is a set of points in three dimensional space.
What else can I help you with?
How many solution sets do systems of linear inequalities have Must solutions to systems of linear inequalities satisfy both inequalities In what case might they not?
A solution to a linear inequality in two variables is an ordered pair (x, y) that makes the inequality a true statement. The solution set is the set of all solutions to the inequality. The solution set to an inequality in two variables is typically a region in the xy-plane, which means that there are infinitely many solutions. Sometimes a solution set must satisfy two inequalities in a system of linear inequalities in two variables. If it does not satisfy both inequalities then it is not a solution.
How is graphing an inequality different from graphing a line on a coordinate plane?
Whereas the procedure for a linear equality is the same, the inequality defines all of the plane on one side (or the other) of the corresponding line.
How is graphing a linear inequality on a coordinate plane different from graphing an inequality on a number line?
The first is 2-dimensional, the second is 1-dimensional.
How do you solve a two variable inequality?
The simplest way is probably to plot the corresponding equality in the coordinate plane. One side of this graph will be part of the feasible region and the other will not. Points on the line itself will not be in the feasible region if the inequality is strict (< or >) and they will be if the inequality is not strict (≤ or ≥). You may be able to rewrite the inequality to express one of the variables in terms of the other. This may be far from simple if the inequality is non-linear.
An equation whose solutions form a straight line on a coordinate plane?
A linear equation.
In the graph of a linear inequality the shaded region above or below the line is called?
The shaded region above or below the line in the graph of a linear inequality is called the solution region. This region represents all the possible values that satisfy the inequality. Points within the shaded region are solutions to the inequality, while points outside the shaded region are not solutions.
How many solutions are there to a linear inequality?
Infinitely many. The solution space is part of a plane.
What is the difference between linear equations and linear inequalities?
It is easiest to describe the difference in terms of coordinate geometry. A linear equation defines a straight line in the coordinate plane. Every point on the line satisfies the equation and no other points do. For a linear inequality, first consider the corresponding linear equality (or equation). That defines a straight line which divides the plane into two. Depending on the direction of the inequality, all points on one side of the line or the other satisfy the equation, and no point from the other side of the line does. If it is a strict inequality (< or >) then points on the line itself are excluded while if the inequality is not strict (≤or ≥) then points on the line are included.
How many solution sets do systems of linear inequalities have Must solutions to systems of linear inequalities satisfy both inequalities In what case might they not?
A solution to a linear inequality in two variables is an ordered pair (x, y) that makes the inequality a true statement. The solution set is the set of all solutions to the inequality. The solution set to an inequality in two variables is typically a region in the xy-plane, which means that there are infinitely many solutions. Sometimes a solution set must satisfy two inequalities in a system of linear inequalities in two variables. If it does not satisfy both inequalities then it is not a solution.
How are quadratic inequalities different from linear inequalities?
A linear inequality is all of one side of a plane. A quadratic inequality is either the inside of a parabola or the outside.
How is graphing an inequality different from graphing a line on a coordinate plane?
Whereas the procedure for a linear equality is the same, the inequality defines all of the plane on one side (or the other) of the corresponding line.
How is graphing a linear inequality on a coordinate plane different from graphing an inequality on a number line?
The first is 2-dimensional, the second is 1-dimensional.
How many points make a plane?
It takes three points to make a plane. The points need to be non-co-linear. These three points define a distinct plane, but the plane can be made up of an infinite set of points.
In the graph of a linear inequality the shaded region above or below the line is called a?
it is called a half plane :)
How do you solve a two variable inequality?
The simplest way is probably to plot the corresponding equality in the coordinate plane. One side of this graph will be part of the feasible region and the other will not. Points on the line itself will not be in the feasible region if the inequality is strict (< or >) and they will be if the inequality is not strict (≤ or ≥). You may be able to rewrite the inequality to express one of the variables in terms of the other. This may be far from simple if the inequality is non-linear.
An equation whose solutions form a straight line on a coordinate plane?
A linear equation.
If three distinct points are not col-linear how many planes can possibly contain the three points?
Three non-co-linear points are sufficient to uniquely define a single plane.
