Define Following:consistent equations
dependent equations
equivalent equations
inconsistent equations
independent equations
no solution
one solution

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

Step-by-step 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

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step-by-step explanation:

steve should create a type of business report called a business plan. the correct option among the options that are already given in the question is the last or the fourth option. this business report created by steve will actually influence the investors about investing their money in steve's business. this business report will have all the details about the business, the amount of investment required and the amount of expected profit.