Question

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

Answer 1

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

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

Explanation:

`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)`