Chapter 6, Problem 12SGR

To determine

To find:The number of solutions of given system of equations using graph and if it hasone solution, name it.

Answer to Problem 12SGR

The given system of equations has one solution $x=1$ , $y=-2$ , and the system is independent.

Explanation of Solution

Given information:

The given system of equations is

  $y=2x-4$

  $4x+y=2$ .

Conceptused:

The point of intersection of two lines is the solution of equations.

If a system has at least one solution, then it is said to be consistent. If a consistent system of equations has exactly one solution, it is independent .

If a consistent system has an infinite number of solutions, it isdependent,when graphed such equations, represent the same line. If a system has no solution, it is said to be inconsistent .The graphs of such equations do not intersect, i.e., graphs are parallel.

Graph:

The graph of given equations $y=2x-4$ , and $4x+y=2$ is shown in Figure-1 here.

From the graph of equations we see that the lines $y=2x-4$ and $4x+y=2$ intersect at point $\left(1,-2\right)$ i.e. the given system of equations has a solution $x=1$ , $y=-2$ , so is consistent. Since, the given system of equations has only one solution so the system is independent.

  

Conclusion:

The given system of equations has one solution $x=1$ , $y=-2$ , and the system is independent.