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Q: Which ordered pairs is a solution of the given system of linear equations?

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The solution to a system on linear equations in nunknown variables are ordered n-tuples such that their values satisfy each of the equations in the system. There need not be a solution or there can be more than one solutions.

there is no linear equations that has no solution every problem has a solution

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

It is a system of linear equations which does not have a solution.

A system of linear equations that has at least one solution is called consistent.

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

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A system of linear equations can only have: no solution, one solution, or infinitely many solutions.

A system of equations may have any amount of solutions. If the equations are linear, the system will have either no solution, one solution, or an infinite number of solutions. If the equations are linear AND there are as many equations as variables, AND they are independent, the system will have exactly one solution.

As there is no system of equations shown, there are zero solutions.

Any solution to a system of linear equations must satisfy all te equations in that system. Otherwise it is a solution to AN equation but not to the system of equations.

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.

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