Question

Solve the following system of equations by graphing. Graph the system below andenter the solution set as an ordered pair in the form (x, y). If there are no solutions,enter None and enter ALL if there are infinite solutions.x - y =1X + y = -7Please see the picture

Answer 1

Given the System of Equations:

`\begin{cases}x-y=1 \\ \\ x+y=-7\end{cases}`

You can graph the lines by finding the x-intercept and the y-intercept of each:

1. Find the x-intercept of each line by substituting this value of "y" into each equation and solving for "x":

`y=0`

Because, by definition, the value of "y" is zero when the line intersects the x-axis.

Then:

- For the first line:

`\begin{gathered} x-0=1 \\ x=1 \end{gathered}`

- For the second line:

`\begin{gathered} x+0=-7 \\ x=-7 \end{gathered}`

2. Find the y-intercept of each line by substituting this value of "x" into each equation and solving for "y":

`x=0`

Because, by definition, the value of "x" is zero when the line intersects the y-axis.

Then:

- For the first line:

`\begin{gathered} 0-y=1 \\ -y=1 \\ y=-1 \end{gathered}`

- For the second line:

`\begin{gathered} 0+y=-7 \\ y=-7 \end{gathered}`

Therefore, you know that the first line passes through these points:

`\mleft(1,0\mright),\mleft(0,-1\mright)`

And the second line passes through these points:

`(-7,0),\mleft(0,-7\mright)`

Knowing these points, you can graph both lines:

Notice that both lines intersect each other at a point. That point is the solution of the System of Equations.

Hence, the answer is:

`\mleft(-3,-4\mright)`