y-axis
(0, 6.5) is one option.
0
-x+y=12is the equation of a line and since there are infinitely many points on the line and each point is represented by an ordered pair, we have infinitely many solutions.If we take x as 0, then y must be 12so (0,12) is one ordered pair that is a solution to the equation.Zero is often a nice number to pick since it makes the calculation a bit easier.
4x-2y=16 has the solution points (0,-8) and (4, 0) at the coordinate axes, and wherever y= 4(x-4).
1
The x-axis
Any with x < 0 and y > 0
To find the ordered pair solution for the equation ( y - 18x - 2 = 0 ), we can rearrange it to express ( y ) in terms of ( x ). This gives us ( y = 18x + 2 ). An ordered pair solution can be obtained by choosing any value for ( x ) and then calculating the corresponding ( y ) value. For example, if ( x = 0 ), then ( y = 2 ), resulting in the ordered pair ( (0, 2) ).
Any ordered pair with the value (x,0) , where x is any number.
Any ordered pair with the value (x,0) , where x is any number.
x = 0 is the y-axis
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.
The pair (2, 3) is the same as the pair (3, 2) but the ORDERED pair (2, 3) is NOT the same as the ORDERED pair (3, 2). In an ordered pair the order of the numbers does matter.
The origin, in the Cartesian coordinate system, is the point with coordinates (0, 0). So, if you have another ordered pair, the ordered pair doesn't "have an origin"; rather, the origin is another point.
(0, 6)
To determine an ordered pair that lies on the graph of the equation (3x + 7y = 11), we can choose a value for (x) and solve for (y). For example, if we let (x = 0), then (3(0) + 7y = 11) simplifies to (7y = 11), giving (y = \frac{11}{7}). Therefore, the ordered pair ((0, \frac{11}{7})) is on the graph of the equation.
The equation ( y = 7x ) defines a linear relationship between ( x ) and ( y ). To find ordered pairs that satisfy this equation, you can choose any value for ( x ) and calculate the corresponding ( y ). For example, if ( x = 1 ), then ( y = 7(1) = 7 ), giving the ordered pair ( (1, 7) ). Similarly, if ( x = 0 ), then ( y = 7(0) = 0 ), resulting in the ordered pair ( (0, 0) ). Other pairs could include ( (2, 14) ) and ( (-1, -7) ).