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Why a linear equation of two variables has an infinite number of solutions?
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.
What are the possible solutions for a pair of linear equation?
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.
Can a linear pair be more or less than 180 degrees?
No. They can only be exactly 180 degrees. By definition, a linear pair is a pair of two adjacent supplementary angles, so together they must form exactly 180 degrees.
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.
Is a linear pair is the same as vertical pair?
no, not exactly.
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.
What are the possible solutions for a pair of linear equation?
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.
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.
Can a linear pair be more or less than 180 degrees?
No. They can only be exactly 180 degrees. By definition, a linear pair is a pair of two adjacent supplementary angles, so together they must form exactly 180 degrees.
What is a solution of a linear equation called?
Ordered Pair * * * * * An ordered SET. There can be only one, or even an infinite number of variables in a linear system.
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.
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.
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)
