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.
That of course will depend on what system of equations are they which have not been given
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)
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.
y = (x + 2)2 andy = (2x)2(x-2)2 + (y-16)2 = 0
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.
To determine the solution to the system of linear equations represented by mc005-1jpg and mc005-2jpg, you would need to solve the equations simultaneously. This typically involves methods such as substitution, elimination, or graphing. Without the specific equations, I cannot provide the ordered pair. Please share the equations for a precise solution.
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.
Tell whether the ordered pair (5, -5) is a solution of the system
The pair of equations have one ordered pair that is a solution to both equations. If graphed the two lines will cross once.
7
That of course will depend on what system of equations are they which have not been given
(-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)
To find the solution to the system of equations ( y = 7x + 2 ) and ( y = 9x - 14 ), set the equations equal to each other: ( 7x + 2 = 9x - 14 ). Solving for ( x ), we get ( 16 = 2x ) or ( x = 8 ). Substituting ( x = 8 ) into either equation gives ( y = 58 ). Thus, the solution is the ordered pair ( (8, 58) ).
To determine which ordered pair is a solution to the linear system defined by the equations ( xy = 2 ) and ( 7x - 4y = 8 ), you can test various pairs. For example, if you try the pair (2, 1), it satisfies the first equation (2 * 1 = 2) and also satisfies the second equation (72 - 41 = 14 - 4 = 10, which is not equal to 8). Therefore, you would need to check other pairs or solve the system algebraically to find the correct solution.
Equations cannot be ordered.
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.
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.
y=(-1) x=(2)