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.
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.
y = (x + 2)2 andy = (2x)2(x-2)2 + (y-16)2 = 0
In the context of Cartesian coordinates, the ordered pair (0, 0) represents a point at the intersection of the x-axis and the y-axis, also known as the origin. The first number in the ordered pair (0) represents the x-coordinate, which is the distance along the horizontal axis from the origin. The second number (0) represents the y-coordinate, which is the distance along the vertical axis from the origin. Therefore, the ordered pair (0, 0) indicates a position where both the x and y coordinates are zero, placing the point at the origin of the coordinate plane.
x = 0 is the y-axis
For example, if you have (0, 6) or (3, 1). Which of them is a solution to y - 2x = 6? Check (0, 6): y - 2x = 6, substitute 0 for x, and 6 for y into the equation 6 - 2(0) =? 6 6 - 0 =? 6 6 = 6 True, then (0, 6) is a solution. Check (3, 1): y - 2x = 6, substitute 3 for x, and 1 for y into the equation 1 - 2(3) =? 6 1 - 6 =? 6 -5 = 6 False, then (3, 1) is not a solution.
One possible solution is x2 + (y - 4)2 = 0.
The equation 2x-5y=-1 has a graph that is a line. Every point on that line is an ordered pair that is a solution to the equation. So pick any real number x and plug it in. You will find a y and that pair (x,y) is an ordered pair that is a solution to this equation. For example, let x=0 Then we have -5y=-1so y=1/5 The ordered pair (0, 1/5) is a point on the line and a solution to the equation.
To determine which ordered pair could be a solution to the inequality (4y - 3x - 2 > 0), you can substitute the values of the ordered pair into the inequality. For example, if we take the ordered pair (1, 2), substituting gives (4(2) - 3(1) - 2 = 8 - 3 - 2 = 3), which is greater than 0, thus (1, 2) is a solution. You can test other pairs similarly to find more solutions.
(0, 6.5) is one option.
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.
To solve the equation (4x + 3y = 6), we can express it in terms of one variable. For example, if we solve for (y), we get (y = \frac{6 - 4x}{3}). An ordered pair solution could be found by choosing a value for (x). For (x = 0), the solution would be ((0, 2)).
12
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.
4x-2y=16 has the solution points (0,-8) and (4, 0) at the coordinate axes, and wherever y= 4(x-4).
(0, 6)
To determine if an ordered pair ((x, y)) is a solution to the inequality (3y - 1 - 2x \geq 0), we can rearrange it to (3y \geq 2x + 1). For example, if we take the ordered pair ((1, 1)), we substitute (x = 1) and (y = 1): (3(1) \geq 2(1) + 1), which simplifies to (3 \geq 3). Since this is true, ((1, 1)) is a valid solution to the inequality.