Question

Solve the system by graphing. Where necessary, indicate when the system has no solution or infinitely many solutions.

y = −2x − 4
−2y = 4x + 8

A.

(0, −4); 

B.

(0, −4); 

C.

(6, 1); 

D.

Infinite solutions; these are equivalent equations.

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Answer 1

The graph is shown below.

D. Infinite solutions; these are equivalent equations.

Explanation:

Given:

The pair of linear equations are:

`y = -2x-4---1\\-2y = 4x + 8---2`

Multiply equation (1) by -2. This gives,

`y* -2 = -2*(-2x-4)\\-2y=4x+8---3`

Now, equations (2) and (3) are same and hence the equations (1) and (2) are the equations of the same line.

In other words, the two lines overlap each other completely. Hence, all the points on the line are the solutions of the given pair of lines. We know that, there are infinitely many points on a line. So, there are infinitely many solutions

The graph is plotted below to support the same.

Therefore, the correct option is option D: Infinite solutions; these are equivalent equations.