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a1 = b1 = c1

a2 = b2 = c2

Q: What are the conditions of consistency for a pair of linear equations?

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The pair of equations have one ordered pair that is a solution to both equations. If graphed the two lines will cross once.

Presumably the question concerned a PAIR of linear equations! The answer is two straight lines intersecting at the point whose coordinates are the unique solution.

By the substitution method By the elimination method By plotting them on a graph

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.

Yes.

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The solution of a system of linear equations is a pair of values that make both of the equations true.

The pair of equations have one ordered pair that is a solution to both equations. If graphed the two lines will cross once.

It deals with lines on a graph, part of an ordered pair ,a steady increase in resultant answer

Presumably the question concerned a PAIR of linear equations! The answer is two straight lines intersecting at the point whose coordinates are the unique solution.

By the substitution method By the elimination method By plotting them on a graph

One option is "cannot exist". The equation is linear and linear equations do not have vertices.

If an ordered pair is a solution to a system of linear equations, then algebraically it returns the same values when substituted appropriately into the x and y variables in each equation. For a very basic example: (0,0) satisfies the linear system of equations given by y=x and y=-2x By substituting in x=0 into both equations, the following is obtained: y=(0) and y=-2(0)=0 x=0 returns y=0 for both equations, which satisfies the ordered pair (0,0). This means that if an ordered pair is a solution to a system of equations, the x of that ordered pair returns the same y for all equations in the system. Graphically, this means that all equations in the system intersect at that point. This makes sense because an x value returns the same y value at that ordered pair, meaning all equations would have the same value at the x-coordinate of the ordered pair. The ordered pair specifies an intersection point of the equations.

The pair of equations: x + y = 1 and x + y = 3 have no solution. If any ordered pair (x,y) satisfies the first equation it cannot satisfy the second, and conversely. The two equations are said to be inconsistent.

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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Yes.

No. All linear pair angles are supplementary, but supplementary angles do not have to be a linear pair.