Question

What is the solution to this system of equations?

Answer 1

The fourth option i.e. 'no solution' is correct.

Explanation:

Given the system of equations

`\begin{bmatrix}(2)/(3)x+y=6\\ -(2)/(3)x-y=2\end{bmatrix}`

Adding both equations

`-(2)/(3)x-y=2`

`+`

`\underline{(2)/(3)x+y=6}`

`0=8`

so the system of equations becomes

`\begin{bmatrix}(2)/(3)x+y=6\\ 0=8\end{bmatrix}`

0 = 8 is FALSE!

Therefore, the system of equations has no solution.

Thus,

No Solution!

Hence, the fourth option i.e. 'no solution' is correct.