Admin Table of Contents
- 1 How do you prove two equations are not equivalent?
- 2 How do you prove something is equivalent?
- 3 What is equivalent and not equivalent?
- 4 What does it mean for two equations to be equivalent?
- 5 What is the condition of no solution?
- 6 What is an not equivalent fraction?
- 7 Are the equations x and Y equivalent?
- 8 What is an equivalent equation with no variables?
How do you prove two equations are not equivalent?
To solve this, you need to find “x” for each equation. If “x” is the same for both equations, then they are equivalent. If “x” is different (i.e., the equations have different roots), then the equations are not equivalent.
How do you prove something is equivalent?
To prove an equivalence relation, you must show reflexivity, symmetry, and transitivity, so using our example above, we can say:
- Reflexivity: Since a – a = 0 and 0 is an integer, this shows that (a, a) is in the relation; thus, proving R is reflexive.
- Symmetry: If a – b is an integer, then b – a is also an integer.
What makes two equations have no solution?
No solution would mean that there is no answer to the equation. It is impossible for the equation to be true no matter what value we assign to the variable. Infinite solutions would mean that any value for the variable would make the equation true. Note that we have variables on both sides of the equation.
What is equivalent and not equivalent?
Nonequivalent fractions are not equal to each other. To determine if two fractions are nonequivalent, you must also cross multiply. For example, to determine if 1/3 and 2/5 are equivalent, you must multiply 1 times 5, which equals 5, and 3 times 2, which equals 6.
What does it mean for two equations to be equivalent?
Two systems of equations are equivalent if they have the same solution(s). Systems of equations that have the same solution are called equivalent systems.
Are two equations equal?
Two equations are said to be equivalent when they have the same solution set. For example, x + 2 = 6 and 2x = 8 are equivalent equations, because when we solve each of them as follows, they have the same solution set. Subtract 2 from both sides. Therefore, the two equations are equivalent.
What is the condition of no solution?
For no solution, Two lines have no solution, if these two lines are parallel to each other. The lines are parallel to each other means that the slopes of the lines are equal. Mathematical representation of the equation with no solution for the given set of general lines is: pu=qv≠rw.
What is an not equivalent fraction?
How do you know if two systems of equations are equivalent?
Given a system of two equations, we can produce an equivalent system by replacing one equation by the sum of the two equations, or by replacing an equation by a multiple of itself. In contrast, we can be sure that two systems of equations are not equivalent if we know that a solution of the one is not a solution of the other.
Are the equations x and Y equivalent?
To answer the question, you could apply the same principles to the second set of equations to solve for “x” and “y” to find that yes, they are indeed equivalent. It’s easy to get bogged down in the algebra, so it’s a good idea to check your work using an online equation solver .
What is an equivalent equation with no variables?
The simplest examples of equivalent equations don’t have any variables. For example, these three equations are equivalent to each other: 3 + 2 = 5 4 + 1 = 5
How do you prove that two things are equivalent?
In general, there are two ways to show that two things are equivalent. You could use logical reasoning, or a truth table. Method 1: logical reasoning For example, you could say (for a smaller case):