Question

What is the solution to this system of equations?

Answer 1

Answer:

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

Step-by-step explanation:

Given the system of equations

$\begin{bmatrix}\frac{2}{3}x+y=6\\ -\frac{2}{3}x-y=2\end{bmatrix}$

Adding both equations

$-\frac{2}{3}x-y=2$

$+$

$\underline{\frac{2}{3}x+y=6}$

$0=8$

so the system of equations becomes

$\begin{bmatrix}\frac{2}{3}x+y=6\\ 0=8\end{bmatrix}$

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.