Question

Solve the system of linear equations by graphing y=x+1 y=-x-3

Answer 1

Solving a system of linear equations by the graphical method consists of representing the equations of the system and the solution of this is the point of intersection between the graphs.

Since a single line passes through 2 points, then to graph the first equation, you can give two arbitrary values to x, replace them in the equation and find their respective y-coordinates.

So if for example, you take x = 1 and x = 2, you have

`\begin{gathered} \text{ If x = 1} \\ y=x+1 \\ y=1+1 \\ y=2 \\ \text{Then, you have the ordered pair} \\ (1,2) \end{gathered}`
`\begin{gathered} \text{If x = 2} \\ y=x+1 \\ y=2+1 \\ y=3 \\ \text{ Then you have the ordered pair (2,3)} \end{gathered}`

Graph the ordered pairs found and join them to obtain the graph of the first equation:

Now do the same with the second equation. If for example, you take x = 0 and x = -1, you have

`\begin{gathered} \text{If x = 0} \\ y=-x-3 \\ y=0-3 \\ y=-3 \\ \text{Then you have the ordered pair (0,-3)} \end{gathered}`
`\begin{gathered} \text{If x = -}1 \\ y=-x-3 \\ y=-(-1)-3 \\ y=1-3 \\ y=-2 \\ \text{ Then, you have the ordered pair (-1,-2)} \end{gathered}`

Graph the ordered pairs found and join them to obtain the graph of the second equation:

Finally, as you can see the graphs of the equations intersect in the ordered pair (-2, -1), therefore the solution of the given system of equations is

`\begin{cases}x=-2 \\ y=-1\end{cases}`