If zero is inserted between the two digits of a two-digit number whose unit's place is $y$ and ten's place is $x$,then the new number is $\ldots \ldots \ldots \ldots$

The angles of a triangle are $x, y$ and $40^{\circ}$. The difference between the two angles $x$ and $y$ is $30^{\circ}$. Find $x$ and $y$.

Graphically,the pair of equations $6x - 3y + 10 = 0$ and $2x - y + 9 = 0$ represents two lines which are:

Solve the following pair of linear equations by the method of substitution: $2x - 3y = -11$ and $4x - 6y + 22 = 0$.

Solve the following pairs of equations by the method of elimination:
$7(y+3)-2(x+2)=14$
$4(y-2)+3(x-3)=2$

Pathik travels $600 \, km$ to his home partly by train and partly by car. He takes $8$ hours if he travels $120 \, km$ by train and the rest by car. He takes $20$ minutes longer if he travels $200 \, km$ by train and the rest by car. Find the speed of the train and the car.