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Which points are solutions to the system of inequalities y is less than 2x y is less than 8 x is greater than 2?
The system of inequalities y<2x, y<8, and x>2 creates a right triangle with points (2,8) (4,8) and (2,4). All the points in this triangle that are whole numbers are:
(2,4) (2,5) (2,6) (2,7) (2,8)
(3,6) (3,7) (3,8)
(4,8)
This set of inequalities and the triangle they form can be visualized at this Desmos graph.
What else can I help you with?
When graphing inequalities where can solutions be found?
I think that you are asking about the linear inequalities with two variables, so my answer is related to them. First, you have to draw the boundary line (be careful, if your inequality does not contain the equal sign, the boundary line will be a dashed line, because the points on the line are not solutions to the inequality), which divide the coordinate system in two half-planes. Second, you have to test a point on either sides of the line (the best point is the origin, (0, 0), if it is not on the boundary line). If that point satisfies the inequality, then there are all its solutions, otherwise they are to the opposite side.
How many solutions does the nonlinear system of equations graphed below have?
2
A system of inequalities cannot involve more than two inequalities?
false
What consists of 2 or more linear inequalities in the same variable?
A system of linear inequalities
When graphing a system of equations what is the point of intersection called?
The points of intersection are normally the solutions of the equations for x and y
Which points are solutions to the system of inequalities?
To determine which points are solutions to a system of inequalities, you need to assess whether each point satisfies all the inequalities in the system. This involves substituting the coordinates of each point into the inequalities and checking if the results hold true. A point is considered a solution if it makes all the inequalities true simultaneously. Graphically, solutions can be found in the region where the shaded areas of the inequalities overlap.
Can the solution of a system of linear inequalities be the points on a line?
yes
How do you determine the solution region for a system of inequalities?
To determine the solution region for a system of inequalities, first graph each inequality on the same coordinate plane. For linear inequalities, use a dashed line for "less than" or "greater than" and a solid line for "less than or equal to" or "greater than or equal to." Shade the region that satisfies each inequality; the solution region is where all shaded areas overlap. This overlapping area represents all the points that satisfy all inequalities in the system.
How do you know if a system has one solution?
If the equations or inequalities have the same slope, they have no solution or infinite solutions. If the equations/inequalities have different slopes, the system has only one solution.
A system of two linear inequalities has either no points or infinitely many points in its solution?
the answer is true
Check all of the points that are solutions to the system of inequalities y 4x plus 3 y -4x plus 6?
the solution for the inequality 4x + 2 - 6x < -1 was x < 3/2
Can every systems of inequalities has a solution?
Not every system of inequalities has a solution. A system of inequalities can be inconsistent, meaning that there are no values that satisfy all inequalities simultaneously. For example, the inequalities (x < 1) and (x > 2) cannot be satisfied at the same time, resulting in no solution. However, many systems do have solutions, which can be represented as a feasible region on a graph.
How is the solution in a system of inequalities determine?
An inequality determines a region of space in which the solutions for that particular inequality. For a system of inequalities, these regions may overlap. The solution set is any point in the overlap. If the regions do not overlap then there is no solution to the system.
How do you know which region of the graph of a system of linear inequalities contains the solutions?
If the lines intersect, then the intersection point is the solution of the system. If the lines coincide, then there are infinite number of the solutions for the system. If the lines are parallel, there is no solution for the system.
How do you solve questions that say which graph best represents the system of inequalities?
The solution to a system of inequalities is where the solutions to each of the individual inequalities intersect. When given a set of graphs look for the one which most closely represents the intersection, this one will contain the most of the solution to the the system but the least extra.
Which of the following points are solutions to the system of inequalities shown below?
y > 5x - 2 y < 5x + 3 A.(4, 20) B.(-5, 25) C.(5, 28) D.(4, 23)
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.
