Question

Four students each wrote an equation. Which two students wrote equations that have no solution?

Answer 1

Beto and Mark

Explanation:

To know which of the equations written by the four students has no solution, let's try to solve each.

Beto's equation:

`3m = 3m + 5`

`3m - 3m = 3m + 5 - 3m`

`0 = 5` (This is incorrect. 0 ≠ 5. This is not a solution)

Lila's Equation:

`9r + 4 = 4 + 9r`

`9r + 4 - 9r = 4 + 9r - 9r`

`4 = 4` (this is correct)

Mark's equation:

`6 - n = -n + 2`

`6 - n + n = -n + 2 + n`

`6 = 2` (incorrect. 6 ≠ 2)

Wanda's Equation:

`8u - 2 = 2u + 8`

`8u - 2 + 2 = 2u + 8 + 2`

`8u = 2u + 10`

`8u - 2u = 2u + 10 - 2u`

`6u = 10`

`(6u)/(6) = (10)/(6)`

`u = (5)/(3)`

If you plug in the value of u into the original equation, the equation would be balanced. Therefore, this is a solution.

Beto and Mark we equations that have no solution.