How do you write a system of equations with the solution (5,8)?

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Answer 1 · 2018-03-19T21:24:15

There are many variations available. It is an extremely open question.

#y=1/2x+11/2#
#y=-2x+18#

#color(blue)("Comment")#

I am choosing to combine two straight line graphs.

If I used a quadratic there could be 2 solutions but the question definitely states THE solution (singular)

What you do is substitute the known common values for #(x,y)=(5,8)# and see what unfolds.
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#color(blue)("Consider the 1st straight line equation")#

#y=mx+c#

I choose to make #m=1/2#

#y=mx+c color(white)("d") ->color(white)("d")8=1/2(5)+c#

Thus #c=8-5/2= 11/2#

So the equation of the straight line is #color(lime)(y=1/2x+11/2)#
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#color(blue)("Consider the 2nd straight line equation")#

This time I choose to make the gradient negative (downward slope)

Set #m=-2#

#y=mx+c color(white)("dd")->color(white)("dd")y=-2x+c color(white)("dd")->color(white)("dd")8=-2(5)+c#

From this #c=8+10=18# giving:

#color(lime)(y=-2x+18)#

Tony B