Answered

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

Sagot :

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

[tex]\begin{gathered} x=2 \\ y=-3 \end{gathered}[/tex]

So, the slope of one equation is 1:

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

Therefore, one of the equations is:

[tex]y-x=-5[/tex]

Now, for the other equation:

[tex]\begin{gathered} y=mx+b \\ x=2 \\ y=-3 \\ -3=2m+b \\ Let \\ b=1 \\ so\colon \\ -3=2m+1 \\ 2m=-4 \\ m=-\frac{4}{2} \\ m=-2 \end{gathered}[/tex]

Therefore, the other equation is:

[tex]2x+y=1[/tex]

Thus, the system of equations is given by:

Answer:

[tex]\begin{gathered} -x+y=-5 \\ 2x+y=1 \end{gathered}[/tex]

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