Question

What was Dimitri's mistake? He mixed up the coordinates of the ordered pair when Substituting it into the equations 7x+9y=-4 and 5x-2y=6

Answer 1

He made a mistake in his calculations when simplifying 5x - 2y

Explanation:

Given

The coordinate pair

`(x,y) = (2,-2)`

The equations

`7x + 9y = ?`

`5x - 2y = ?`

Dimitri's Solution

`Equation\ 1: 7x + 9y = -4.`

`7(2) + 9 (-2) = -4.`

`14 + (-18) = -4.`

`-4 = -4.`

`Equation\ 2: 5x -2y = 6.`

`5(2) - 2 (-2) = 6.`

`10 - 4 = 6.`

`6 = 6.`

Required

Identify Dimitri’s mistake

In the first equation, Dimitri made no mistake.

However, he made a mistake when simplifying the second equation.

We have:

`5x - 2y`

and

`(x,y) = (2,-2)`

Substitute
`x = 2` and
`y = -2`

So, we have:

`5(2) -2(-2)`

Open bracket

`10 +4`

Finally, we have:

`14`