Chapter ISG, Problem 6.1.2.3P

To determine

To solve the system of equations graphically.

Answer to Problem 6.1.2.3P

No solutions.

Explanation of Solution

Given information:

  $\begin{array}{l}2y=5+x\\ 3x-6y=-15\end{array}$

Calculation:

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

Taking (1)

  $2y=5+x$

Rearranging,

  $x=2y-5$   -(3)

Putting in (2)

  $3(2y-5)-6y=-15$

Solving equation,

  $6y-15-6y=-15$

So,

  $6y-6y=-15+15$

  $0=0$

Hence, left hand side= right hand side

From this statement, we can conclude that both line overlaps. Hence, the solutions of this system of equation is infinite.

Graph:

Blue line represents: $2y=5+x$

Orange line represents: $3x-6y=-15$