Infinite.
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.
1
Inequalities tend to have infinitely many solutions.
None, one or infinitely many.
A linear equation in two variables represents a straight line on a Cartesian plane. Each point on this line corresponds to a unique pair of values for the two variables that satisfy the equation. Since there are infinitely many points on a line, there are also infinitely many solutions to the equation. Thus, any linear equation in two variables has an infinite number of solutions.
Infinitely many.
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.
A single linear equation in two variables has infinitely many solutions. Two linear equations in two variables will usually have a single solution - but it is also possible that they have no solution, or infinitely many solutions.
Infinitely many. The solution space is part of a plane.
1
Inequalities tend to have infinitely many solutions.
None, one or infinitely many.
A linear equation in two variables represents a straight line on a Cartesian plane. Each point on this line corresponds to a unique pair of values for the two variables that satisfy the equation. Since there are infinitely many points on a line, there are also infinitely many solutions to the equation. Thus, any linear equation in two variables has an infinite number of solutions.
The area in the inequality gives you choices. Like the number of pounds that an elevator can carry is anything less than its maximum.
No, a linear equation in two variables typically has one unique solution, which represents the intersection point of two lines on a graph. However, if the equation represents the same line (as in infinitely many solutions) or if it is inconsistent (no solutions), then the type of solutions can vary. In general, a single linear equation corresponds to either one solution, no solutions, or infinitely many solutions when considering the same line.
2
There are infinitely many solutions. One linear equation in two variables cannot be solved to give a single answer.