Question

Define Following:consistent equations

dependent equations
equivalent equations
inconsistent equations
independent equations
no solution
one solution

Answer 1

Consistent Equation - two or more equations that have at least one common solution

Dependent Equation - If a consistent system has an infinite number of solutions, it is dependent . When you graph the equations, both equations represent the same line

Equivalent Equations - equations that have the same solutions

Inconsistent Equations - If a system has no solution, it is said to be inconsistent

Independent Equations - If a consistent system has exactly one solution, it is independent

No Solution - 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

One solution - no matter what constant is substituted in for the variable, the equation is always true. No matter what constant is substituted in for the variable, the equation will never be true. Only this one solution will make the equation true.

Explanation:

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Answer 2

1. Consistent equations

x + y = 3

x + 2·y = 5

2. Dependent equations

3·x + 2·y = 6

6·x + 4·y = 12

3. Equivalent equations

9·x - 12·y = 6

3·x - 4·y = 2

4. Inconsistent equations

x + 2 = 4 and x + 2 = 6

5. Independent equations

y = -8·x + 4

8·x + 4·y = 0

6. No solution

4 = 2

7. One solution

3·x + 5 = 11

x = 2

Explanation:

1. Consistent equations

A consistent equation is one that has a solution, that is there exist a complete set of solution of the unknown values that resolves all the equations in the system.

x + y = 3

x + 2·y = 5

2. Dependent equations

A dependent system of equations consist of the equation of a line presented in two alternate forms, leading to the existence of an infinite number of solutions.

3·x + 2·y = 6

6·x + 4·y = 12

3. Equivalent equations

These are equations with the same roots or solution

e.g. 9·x - 12·y = 6

3·x - 4·y = 2

4. Inconsistent equations

Inconsistent equations are equations that are not solvable based on the provided set of values in the equations

e.g. x + 2 = 4 and x + 2 = 6

5. Independent equations

An independent equation is an equation within a system of equation, that is not derivable based on the other equations

y = -8·x + 4

8·x + 4·y = 0

6. No solution

No solution indicates that the solution is not in existence

Example, 4 = 2

7. One solution

This is an equation that has exactly one solution

Example 3·x + 5 = 11

x = 2