Systems of Linear Equations and Inequalities

1003020302

Level: 
A
Assuming \( [x;y]\in\mathbb{R}\times\mathbb{R} \), solve the equation \[ x-y-\frac{x-y}2=\frac{x-y}3 \] Decide which of the answers below does not express the set of roots.
\( \left\{[x;y],x\in\mathbb{R},y\in\mathbb{R}\right\} \)
\( \left\{[x;x],x\in\mathbb{R}\right\} \)
\( \left\{[y;y],y\in\mathbb{R}\right\} \)
\( \left\{[t;t],t\in\mathbb{R}\right\} \)

1003020301

Level: 
A
In \( \mathbb{R}\times\mathbb{R} \), find the solution set of the equation: \[ 2x-\frac{x+2y}3=2+\frac83y \]
\( \left\{\left[2y+\frac65;y\right],y\in\mathbb{R}\right\} \)
\( \left\{\left[2y+\frac65;\frac x2-\frac35\right],x\in\mathbb{R},y\in\mathbb{R}\right\} \)
\( \left\{\left[\frac{6+6y}5;y\right],y\in\mathbb{R}\right\} \)
\( \emptyset \)