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Any system of linear equations can have the following number of solutions:
0 if the system is inconsistent (one of the equations degenerates to 0=1)
1 if the system is linearly independent
infinity if the system has free variables and is not inconsistent.
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Can a pair of linear equation have exactly two solutions?
No. A pair of linear equation can have 0 solutions (they are parallel), or one solution (they cross at one point) or an infinite number of solutions (they represent the same line).
Can a pair of linear angles form a linear pair?
Yes.
Are supplementary angles necessarily a linear pair?
No. All linear pair angles are supplementary, but supplementary angles do not have to be a linear pair.
Do all supplementary angles from a linear pair Are all linear pair supplementary?
All supplementary angles do not form a linear pair. The opposite angles of any quadrilateral inscribed in a circle (a cyclic quadrilateral) are supplementary but they are not a linear pair. However, all linear pair are supplementary.
What solution does a negative discriminant have?
In basic mathematics, a quadratic equation with a negative discriminant has no solutions. However, at a more advanced level you will learn that it has two solutions which form a complex conjugate pair.
Can a pair of linear equation have exactly two solutions?
No. A pair of linear equation can have 0 solutions (they are parallel), or one solution (they cross at one point) or an infinite number of solutions (they represent the same line).
What does it mean for a ordered pair to be a solution to a linear equation?
An ordered pair is a solution only of a linear equation in two variables - not any linear equation. Often the variables are denoted by x and y. If the first of the ordered pair is substituted for x in the equation, and the second for y, then the equation represents a true statement.
Which ordered pair is a solution of the linear system?
This is a linear algebra question and it is incomplete since there are no equation which have to be solved.
Is it possible for 3 angles to form a linear pair?
No, "pair" implies two and only two.
What is a solution of a linear equation called?
A solution of a linear equation is called a root or a solution. It is a value that satisfies the equation when substituted back into it.
Which word pair is the vertex of y equals x plus 4?
One option is "cannot exist". The equation is linear and linear equations do not have vertices.
What is y equals 1x plus 6?
It is a linear equation in the two variables x and y. A single linear equation in two variables cannot be solved for a unique pair of values of x and y. The equation is that of a straight line and any point on the line satisfies the equation.
Can a pair of linear angles form a linear pair?
Yes.
Are supplementary angles necessarily a linear pair?
No. All linear pair angles are supplementary, but supplementary angles do not have to be a linear pair.
Which ordered pair is a solution of the equation 2x - 3y equals 18?
There are an infinite number of solutions to this equation, some of which are (9,0), (12,2), (15,4), (18,6), (21,8)
What are the integer solutions to x to the y'th equals y to the x'th?
If x = y, then the equation is true for any integer pair. Otherwise, the equation is not equivalent and is impossible.
Do all supplementary angles from a linear pair Are all linear pair supplementary?
All supplementary angles do not form a linear pair. The opposite angles of any quadrilateral inscribed in a circle (a cyclic quadrilateral) are supplementary but they are not a linear pair. However, all linear pair are supplementary.
