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Q: How can you determine if the given ordered pair is a solution to the system of equations?

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Tell whether the ordered pair (5, -5) is a solution of the system

That would be the "solution" to the set of equations.

an ordered pair that makes both equations true

That would depend on the given system of linear equations which have not been given in the question

That of course will depend on what system of equations are they which have not been given

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.

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

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.

7

You substitute the coordinates of the point in the equation. If the result is true then the point is a solution and if it is false it is not a solution.

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

A system of equations with exactly one solution intersects at a singular point, and none of the equations in the system (if lines) are parallel.

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

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.

If a system has no solution, it means that the lines are parallel.

A system of equations will have no solutions if the line they represent are parallel. Remember that the solution of a system of equations is physically represented by the intersection point of the two lines. If the lines don't intersect (parallel) then there can be no solution.

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

Graph both equations on the same graph. Where they intersect is the solution to the system of 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.

No It;s Not A Solution > :)

No because there are no equations there to choose from.

The solution is the coordinates of the point where the graphs of the equations intersect.

No

visual,intuitive

Inconsistent.

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