Question : If $( x^{3}-y^{3}):( x^{2}+xy+y^{2})=5:1$ and $( x^{2}-y^{2}):(x-y)=7:1$, then the ratio $2x:3y$ equals:

Option 1: $4:1$

Option 2: $2:3$

Option 3: $4:3$

Option 4: $3:2$

Question : The graphs of the equations
$4 x+\frac{1}{3} y=\frac{8}{3}$ and $\frac{1}{2} x+\frac{3}{4} y+\frac{5}{2}=0$ intersect at a point P. The point P also lies on the graph of the equation:

Option 1: $x + 2y - 5 = 0$

Option 2: $3x - y - 7 = 0$

Option 3: $x - 3y - 12= 0$

Option 4: $4x - y + 7= 0$

Question : If $x^2-xy+y^2=2$ and $x^4+x^2y^2+y^4=6$, then the value of $(x^2+xy+y^2)$ is:

Option 1: 1

Option 2: 12

Option 3: 3

Option 4: 36

Question : If $x+3y=-3x+y$, then $\frac{x^{2}}{2y^{2}}$ is equal to:

Option 1: $\frac{1}{8}$

Option 2: $\frac{1}{2}$

Option 3: $\frac{1}{4}$

Option 4: $4$

Question : What is the solution of the following equations?
2x + 3y = 12 and 3x – 2y = 5

Option 1: x = 3, y = 2

Option 2: x = 2, y = 3

Option 3: x = –2, y = 3

Option 4: x = 3, y = –2