Chapter ISG, Problem 6.1.2.2P

To determine

To solve the system of equations graphically.

Answer to Problem 6.1.2.2P

No solutions.

Explanation of Solution

Given information:

  $\begin{array}{l}2x+y=4\\ y=-2x-2\end{array}$

Calculation:

Let us assume the equations to be (1) and (2) respectively,

Rearranging (2),

  $2x+y=-2$

Taking (1)

  $2x+y=4$   -(3)

Solving,

  $2x=4-y$

Put in (3)

  $4-y+y=-2$

Solving,

  $4\ne 2$

Left hand side is not equal to right hand side.

The system of equation has no solution because, they are parallel lines. It means they have no intersecting point. Hence, no solution.

Graph:

Blue line represents: $2x+y=4$

Orange line represents: $2x+y=-2$