Chapter ISG, Problem 6.1.2.4P

To determine

To solve the system of equations graphically.

Answer to Problem 6.1.2.4P

  $x=1$ and $y=7$

Explanation of Solution

Given information:

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

Calculation:

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

Taking (1)

  $2x-y=-5$

Re-arranging the equation,

  $y=2x-5$   -(3)

Taking equation (2)

  $x+y=-2$

Substituting values of (3) to equation,

  $x+2x-5=-2$

Solving,

  $\begin{array}{l}3x-5=-2\\ 3x=3\end{array}$

Dividing equation by 3

  $x=1$   -(4)

Putting (4) in (1)

  $2(1)-y=-5$

Solving equation,

  $\begin{array}{l}2-y=-5\\ -y=-7\end{array}$

Dividing by -1,

  $y=7$

Hence, $x=1,y=7$ is the solution of graph.

Verifying the solution,

Put values of $x$ and y in function.

  $2(1)-5=-3$

Left hand side= right hand side.

Hence, solution is correct.

Graph:

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

Orange line represents: $2x-y=-5$