Question

Which of the ordered pairs (6, 1), (10, 0), (6, –1), (–22, 8) are solutions for the equation x + 4y = 10?

Answer 1

`S={(6,1);(10,0);(-22,8)}`

Explanation:

An ordered pair is solution for an equation when your equality is true for this pair.

Let `x+4y=10` ,
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Is `(6,1)` a solution for `x+4y=color(green)10` ?

Replace in the equality `color(red)x` by `color(red)6` and `color(blue)y` by `color(blue)1`

`x+4y=color(red)6+4*color(blue)1color(green)(=10)`

Yes, `(6,1)` is a solution of `x+4y=10`
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Is `(6,-1)` a solution for `x+4y=10` ?

Replace in the equality `color(red)x` by `color(red)6` and `color(blue)y` by `color(blue)(-1)`

`x+4y=color(red)6+4*color(blue)((-1))=color(grey)2color(red)!=color(grey)10`

No, `(6,-1)` isn't a solution of `x+4y=10`
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For training, you can check that `(10,0)` and `(-22,8)` are solutions of `x+4y=10`.