Solve the simultaneous equations.

$x+2y=5$ and $x^2+y^2=10$

Solve the simultaneous equations.

$x-12y=30$ and $2y^2-xy=20$

The sum of two numbers is $26.$ The product of the two numbers is $153$.

What are the two numbers?

The sum of two numbers is $26.$ The product of the two numbers is $150$, what would be the two numbers?

The perimeter of a rectangle is $15.8 \mathrm{cm}$ and its area is $13.5 {\mathrm{cm}}^2$ Find the lengths of the sides of the rectangle.

The sum of the perimeters of two squares is $50 \mathrm{cm}$ and the sum of the areas is $93.25{ \mathrm{cm}}^2$. Find the side length of each square.

The sum of the circumferences of two circles is $36\pi \mathrm{cm}$ and the sum of the areas is $170\pi {\mathrm{cm}}^2$. Find the radius of each circle.

A cuboid has sides of length $5 \mathrm{cm}, x \mathrm{cm}$ and $y \mathrm{cm}$. Given that $x+y=20.5$ and the volume of the cuboid is $360{ \mathrm{cm}}^3$, find the value of $x$ and the value of$y$ .

The diagram shows a solid formed by joining a hemisphere, of radius $r \mathrm{cm}$, to a cylinder, of radius $r \mathrm{cm}$ and height $h \mathrm{cm}$. The total height of the solid is$18 \mathrm{cm}$ and the surface area is $205\pi {\mathrm{cm}}^2$. Find the value of $r$ and the value of $h$.