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.2 – y=1x +y = -7y

Answer 1

The solution to the system of equations is:

x = -3

y = -4

The ordered pair form is: (-3, -4)

Solution

- The question tells us to find the solution to the system of equations:

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

- To find the solution to the system of equations, we will apply the elimination method. This method entails adding and subtracting both equations in order to find the values of x and y.

- We can thus proceed to solve the question as follows:

Finding the value of x:

`\begin{gathered} x-y=1 \\ x+y=-7 \\ \\ \text{Add both equations together} \\ x-y+(x+y)=1+(-7) \\ x-y+x+y=1-7 \\ 2x=-6 \\ \text{Divide both sides by 2} \\ (2x)/(2)=-(6)/(2) \\ \\ \therefore x=-3 \end{gathered}`

Finding the value of y:

`\begin{gathered} x-y=1 \\ x+y=-7 \\ \\ \text{Subtract both equations} \\ x-y-(x+y)=1-(-7) \\ x-y-x-y=1+7 \\ -2y=8 \\ \text{Divide both sides by -2} \\ -(2y)/(-2)=(8)/(-2) \\ \\ \therefore y=-4 \end{gathered}`

Final Answer

The solution to the system of equations is:

x = -3

y = -4

The ordered pair form is: (-3, -4)