Chapter ISG, Problem 6.1.2.1P

To determine

To solve the system of equations graphically.

Explanation of Solution

Given information:

  $\begin{array}{l}2x-y=-3\\ 2x+y=-1\end{array}$

Calculation:

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

Taking (1)

  $2x-y=-3$

Re-arranging the equation,

  $y=2x+3$   -(3)

Taking equation (2)

  $2x+y=-1$

Substituting values of (3) to equation,

  $2x+(2x+3)=-1$

Solving,

  $\begin{array}{l}4x+3=-1\\ 4x=-4\end{array}$

Dividing equation by 4

  $x=-1$   -(4)

Putting (4) in (1)

  $2(-1)-y=-3$

Solving equation,

  $\begin{array}{l}-2-y=3\\ y=-2+3\end{array}$

So,

  $y=1$

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

Verifying the solution,

Put values of $x$ and y in function.

  $2(-1)-1=-3$

And,

  $-2-1=-3$

Left hand side= right hand side.

Hence, solution is correct,.

Graph:

Blue line represents: $2x-y=-3$

Orange line represents: $2x+y=-1$