Dimension. Lines, line segments, and rays are all one-dimensional objects: in order to have the concept of a line make sense in an argument, the context in which you are arguing must have at least one dimension.

Two-dimensional art processes and techniques are those that are created on a flat plane. They have height and width, but not significant depth. These include drawing, printmaking, painting, photography, and some mixed media.

When something is described as 2-dimensional, it has measurable length and width but no depth. A shape is a defined 2-dimensional area. The two types of shapes are geometric and free-form, which differ in the contours they are characterized by.

Answer Expert Verified Out of the choices, the entities with only one dimension and have infinite length are the line and ray. The line extends to both sides while the ray is restricted by an endpoint on one side but can extend infinitely to the other side.

Vocabulary Language: English ▼ English

Now the test for perpendicularity is that the dot product of the direction vectors of the 2 lines has to be 0. Remember if the dot product of 2 vectors is 0 they’re perpendicular. So if the direction vector is, of 2 lines are perpendicular then the lines are perpendicular.

We can determine from their equations whether two lines are parallel by comparing their slopes. If the slopes are the same and the y-intercepts are different, the lines are parallel. If the slopes are different, the lines are not parallel. Unlike parallel lines, perpendicular lines do intersect.

Two lines are perpendicular if and only if the product of their slopes is . In other words, the slope of a line that is perpendicular to a given line is the negative reciprocal of that slope. Thus, for a line with a given slope of 3, the line perpendicular to that slope must be the negative reciprocal of 3, or .

If two lines are parallel then, they have no solution pair of linear equations is inconsistent; If two lines are coincident then, they have infinite solution and pair of linear equations is consistent; If two lines are intersecting then, they have unique solution and pair of linear equations is consistent.

Two lines in a plane are said to be parallel if they do not intersect, when extended infinitely in both the direction. Also, the distance between the two lines is the same throughout.

A system has no solutions if the lines are parallel. When solving the system, if you get a false statement (a number equal to a different number) this means there are no solutions.

A system has no solution if the equations are inconsistent, they are contradictory. for example 2x+3y=10, 2x+3y=12 has no solution. is the rref form of the matrix for this system.

When a problem has infinite solutions, you’ll end up with a statement that’s true no matter what. For example: 3=3 This is true because we know 3 equals 3, and there’s no variable in sight. Therefore we can conclude that the problem has infinite solutions. You can solve this as you would any other equation.

The constants are the numbers alone with no variables. If the coefficients are the same on both sides then the sides will not equal, therefore no solutions will occur. Use distributive property on the right side first.

Well, there is a simple way to know if your solution is an infinite solution. An infinite solution has both sides equal. For example, 6x + 2y – 8 = 12x +4y – 16. If you simplify the equation using an infinite solutions formula or method, you’ll get both sides equal, hence, it is an infinite solution.

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For an answer to have an infinite solution, the two equations when you solve will equal 0=0 . Here is a problem that has an infinite number of solutions. If you solve this your answer would be 0=0 this means the problem has an infinite number of solutions.

Condition for Unique Solution to Linear Equations A system of linear equations ax + by + c = 0 and dx + ey + g = 0 will have a unique solution if the two lines represented by the equations ax + by + c = 0 and dx + ey + g = 0 intersect at a point. i.e., if the two lines are neither parallel nor coincident.

By the term unique solution, one mean to say that only one specific solution set exists for a given equation. So, if we have two equations, then unique solution will mean that there is one and only point at which the two equations intersect.

You will be able to determine if an equation has one solution (which is when one variable equals one number), or if it has no solution (the two sides of the equation are not equal to each other) or infinite solutions (the two sides of the equation are identical).

In order for a linear system to have a unique solution, there must be at least as many equations as there are variables. The solution to a system of linear equations in two variables is any ordered pair (x,y) that satisfies each equation independently. Graphically, solutions are points at which the lines intersect.

In a two-variable problem rewrite the equations so that when the equations are added, one of the variables is eliminated, and then solve for the remaining variable. Step 1: Multiply equation (1) by -5 and add it to equation (2) to form equation (3) with just one variable.

The standard form for linear equations in two variables is Ax+By=C. For example, 2x+3y=5 is a linear equation in standard form.