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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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Q: What does it mean both algebraically and graphically when an ordered pair is a solution to a system of two linear equations?

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Plug your ordered pair into both of your equations to see if you get they work.

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

an ordered pair that makes both equations true

Always. Every ordered pair is the solution to infinitely many equations.

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

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.

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

7

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

Equations cannot be ordered.

(-4,-5)

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.

(10, 2)

I'm guessing that you're looking at an ordered pair AND a list of equations. Since I can't see either of them, my chances of matching them up are not looking too promising.

y=(-1) x=(2)

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.

(0,7)

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

Do you mean: 4x+7y = 47 and 5x-4y = -5 Then the solutions to the simultaneous equations are: x = 3 and y = 5

with ur partner

8

Use the substitution method to solve the system of equations. Enter your answer as an ordered pair.y = 2x + 5 x = 1

y = (x + 2)2 andy = (2x)2(x-2)2 + (y-16)2 = 0

there are none, ordered pairs come from equations like x = 2y -5

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