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What does it mean both algebraically and graphically when an ordered pair is a solution to a system of two linear equations?
Wiki User
∙ 14y ago
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.
Wiki User
∙ 14y ago
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Malique solved the system of equations below and found that x 5 which ordered pairs is the solution to the system?
That of course will depend on what system of equations are they which have not been given
How is a system of 2 linear equations have no solution?
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.
What is the ordered pair the is th solution to these equations x equals 5y and 2x - 3y equals 14?
(10, 2)
Is the ordered pair 0 -6 solution for y5x-7?
The ordered pair (0, -6) Ordered pairs look like (x, y). they are the coordinates of a point on your graph. Asking if (0,6) is a solution to your equation means, does this point lie on the graph? Or algebraically, if you substitute in x = 0 and y = -6 into the equation, does it work? y = 5x-7 -6 = 5(0) -7 -6 = 0 - 7 -6 = -7 Well, -6 does NOT = -7, so we know that this ordered pair is not a solution to the function.
The ordered pair 2 16 is a solution for which of the following equations?
y = (x + 2)2 andy = (2x)2(x-2)2 + (y-16)2 = 0
How can you determine if the given ordered pair is a solution to the system of equations?
Plug your ordered pair into both of your equations to see if you get they work.
What is an ordered pair that makes all equations in a system true?
That would be the "solution" to the set of equations.
What is a solution to a system?
an ordered pair that makes both equations true
When is it possible for an ordered pair to be the solution of more than one equation?
Always. Every ordered pair is the solution to infinitely many equations.
Which ordered pairs is a solution of the given system of linear equations?
That would depend on the given system of linear equations which have not been given in the question
What is the solution to a linear equation?
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.
Describe a consistent independent system of linear equations?
The pair of equations have one ordered pair that is a solution to both equations. If graphed the two lines will cross once.
Determine if the ordered pair y3x 5 yx 9 211 isa solution to the system of equations?
Tell whether the ordered pair (5, -5) is a solution of the system
What is the solution of the system of linear equations x equals 5 y equals -2?
7
Malique solved the system of equations below and found that x 5 which ordered pairs is the solution to the system?
That of course will depend on what system of equations are they which have not been given
Type the ordered pair that is the solution to these equations.2x - 3y = 7-3x + y = 7?
(-4,-5)
How is a system of 2 linear equations have no solution?
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.
