WorksheetsSystem of Linear Inequalities in Two Variables
Total questions: 25
Worksheet time: 18mins
Which of the following represents a system of linear inequalities in two variables?
x + y ≤ 5
3x + 2y=10
2x − 3y > 7
y ≥ 2x + 3
How many solutions can a system of linear inequalities have?
One solution
Infinite solutions
Two solutions
No solution
If the solution to system of linear inequalities is a shaded region in a graph, what does this shaded region represent?
The possible values that satisfy both inequalities
The x-intercepts of the inequalities
The impossible values that satisfy both inequalities
The y-intercepts of the inequalities
Which method can be used to solve a system of linear inequalities?
Substitution
Graphing
Elimination
All of the above
What does it mean if a point lies on the boundary line of a system of linear inequalities?
It is a solution to the system
It is part of the feasible region
It is not a solution to the system
It is an invalid point
Which of the following represents a system of linear inequalities with no solution?
x + y ≥ 5 and x + y ≤ 3
3x + 2y ≥ 10 and 3x + 2y ≤ 5
2x−3y > 7 and 4x−6y > 14
y ≤ 2x+3 and y > 2x+3
How can you determine if a point is a solution to a system of linear inequalities?
Plug the point into both inequalities and see if they are true
Check if the point is on the x-axis
Only plug the point into one of the inequalities
Check if the point is on the y-axis
What is the solution to the system of linear inequalities: y ≥ −2x+4 and y ≤ 3x+1 ?
(−1,6)
(0,4)
(2,5)
(3,7)
Which of the following represents the feasible region of a system of linear inequalities?
The x-intercepts of the inequalities
The region outside the shaded area
The region inside the shaded area
The y-intercepts of the inequalities
When solving a linear inequalities algebraically, what does it mean if you arrive at a FALSE statement like 0 > 5 ?
The system has no solution
The system has exactly one solution
The system has infinite solutions
The system cannot be solved algebraically
A solution to a system of linear inequalities is a point that satisfies all the inequalities in the system.
True
False
In a linear inequalities, shading the region that satisfies all the inequalities will give the feasible region.
True
False
If a system of linear inequalities has a solution, it will always be a bounded region.
True
False
A system of linear inequalities can have exactly two solutions.
True
False
The solution to a system of linear inequalities is always a region on the coordinate plane.
True
False
The solution to a system of linear inequalities can never be a single point.
True
False
Graphically, the solution to a system of linear inequalities is the area where all shaded regions overlap.
True
False
The graphical method for solving systems of linear inequalities involves shading the region where the inequalities are greater than or equal to zero.
True
False
If the system of linear inequalities has three inequalities, the feasible region will be a triangle.
True
False
Solving a system of inequalities involves finding the values of the variables that satisfy one inequality at a time.
True
False
The solution to a linear inequality in two variables often represents a (a) region on a coordinate plane.
To test which side of a line to shade when solving a linear inequality, we often use the point (0,0), also known as the (a) .
A point that satisfies the inequality but lies on the boundary line is called a (a) point.
When solving systems of linear inequalities, the solution is the (a) of all the individual solution sets.
A point that does not satisfy the inequality when plugged into it is called a (a) point.
