Question

For the graph shown, select the statement that best represents the given system of equations.

5y – 7x = 10 3y 4x = 6
A. not enough information
B. coincident
C. consistent and independent
D. inconsistent

Answer 1

the answer is C.consistent and independent

Answer 2

Answer: The statement 'C. Consistent and independent' best represents the given system of equation.

Explanation:

If a system of equations has at least one solution then it is called consistent while if it does not have any solution then it is called inconsistent.

The consistent system further divides into two types,

Independent : If a consistent system has exactly one solution.

Dependent : If a consistent system has infinitely many solutions.

Here, the given system of equations,

5y - 7x = 10,

3y + 4x = 6,

Since, by solving these equations,

We get, x = 0 and y = 2,

Hence, the solution of the given system of equations is (0,2) ( also shown in the graph )

By the above definition,

⇒ It is an independent consistent system.

⇒ Option C is correct.