systems of linear equations
What is the solution to this set of linear equations?
2x + 3y = 11
x - y = 2
(3.4, 1.4)
Graph the system of inequalities and provide 2 possible solutions:
[y > x]
[y < 2x]
Answers vary
What are you looking for when finding solutions to a system of inequalities?
The shaded regions that overlap.
Solve the following system of equations:
[3x - y = 2]
[2x + y = 1]
(.6, -0.2)
In the sequence 2, 4, 6, 8, what is the common difference?
d = 2
Find the solution to the system of equations:
[3x + 4y = 8]
[2x - y = 5]
(2.54, .09)
A solid line is used when...?
less than or equal to OR greater than or equal to
Determine if the point (2, 2) is a solution to the system of inequalities:
[x + y < 4] [2x - y >= 0]
No
What is the solution to the system of equations?
x = 5
y = -3
(5, -3)
Given the sequence 3, 6, 12, 24, what is the next term?
48
A system of equations has no solution when…?
The lines are parallel.
Do you include points on a dashed line as part of the solution set?
No, you do not include points on a dashed line.
Explain what it means for a point to be a viable solution in the context of a system of linear inequalities.
Answers vary: for a solution to be viable, it needs to make both inequalities true and fall in the area where both sets of inequalities shading overlaps
What is the solution to a system of linear equations when both lines have the same slope?
no solution
In a relation, if each input is paired with exactly one output, it is called:
a. A function
b. A linear relation
c. An inverse function
d. A non-linear relation
a. a function
A system has one solution when...?
The lines intersect.
If a point falls on a solid line, is it included in the solution set?
Yes - it is included in the solution set because it is on the solid line, which is inclusive. The points on the solid line are included in the solution set.
How could you determine if a point is a solution without graphing?
Answers vary: the x and y of the point should satisfy both equations and make them true
How can you verify the solution obtained from graphing a system of linear equations?
Which of the relations below is NOT a function?
a. {(1, 3), (2, 5), (3, 3)}
b. {(2, 4), (5, 7), (2, 6)}
c. {(1, 2), (2, 1), (3, 5)}
d. {(4, 7), (7, 5), (2, 9)}
b. {(2, 4), (5, 7), (2, 6)}
When there are 2 equations for the same line, the answer is...?
Infinitely many solutions
In the inequality y<2x-1, will (0,0) make this inequality true?
No the solution would give you 0<-1 therefore the point would not be true.
What is a/the solution to this set of inequalities?
y >-2x +1
y - 1 > -2x
infinitely many solutions
What are the equations for this system of linear equations?
(Capture 7)
y = 4x + 2
y= -2x+3
What is the first term in an arithmetic sequence if the common difference is 5 and the 5th term is 23?
a. 5
b. 8
c. 10
d. 3
d - 3