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

1 Answer
Mar 19, 2018

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

y=1/2x+11/2y=12x+112
y=-2x+18y=2x+18

Explanation:

color(blue)("Comment")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)(x,y)=(5,8) and see what unfolds.
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color(blue)("Consider the 1st straight line equation")Consider the 1st straight line equation

y=mx+cy=mx+c

I choose to make m=1/2m=12

y=mx+c color(white)("d") ->color(white)("d")8=1/2(5)+cy=mx+cdd8=12(5)+c

Thus c=8-5/2= 11/2c=852=112

So the equation of the straight line is color(lime)(y=1/2x+11/2)y=12x+112
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color(blue)("Consider the 2nd straight line equation")Consider the 2nd straight line equation

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

Set m=-2m=2

y=mx+c color(white)("dd")->color(white)("dd")y=-2x+c color(white)("dd")->color(white)("dd")8=-2(5)+cy=mx+cddddy=2x+cdddd8=2(5)+c

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

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

Tony B