Question

Write a system of equations that satisfies each condition below: One solution at (2,-3) The slope of one equation is 1.

Answer 1

Since one of the solutions is at (2,-3):

`\begin{gathered} x=2 \\ y=-3 \end{gathered}`

So, the slope of one equation is 1:

`\begin{gathered} y=mx+b \\ m=1 \\ x=2 \\ y=-3 \\ -3=1(2)+b \\ -3=2+b \\ b=-5 \end{gathered}`

Therefore, one of the equations is:

`y-x=-5`

Now, for the other equation:

`\begin{gathered} y=mx+b \\ x=2 \\ y=-3 \\ -3=2m+b \\ Let \\ b=1 \\ so\colon \\ -3=2m+1 \\ 2m=-4 \\ m=-(4)/(2) \\ m=-2 \end{gathered}`

Therefore, the other equation is:

`2x+y=1`

Thus, the system of equations is given by:

Answer:

`\begin{gathered} -x+y=-5 \\ 2x+y=1 \end{gathered}`