Simultaneous Linear Equations：練習問題

If \(2x + y = 5\) and \(y = 3\), what is the value of \(x\)?

The perimeter of a rectangle is \(24\text{ cm}\). If its length is \(2\text{ cm}\) longer than its width, find the area of the rectangle.

The ratio of the price of a burger to a soda is \(5:2\). If a customer buys 2 burgers and 3 sodas, the total cost is \(\$64\). Find the price of one burger.

Solve the following simultaneous linear equations for \(y\):
\(x + 4y = 18\)
\(x - y = 3\)

A shop sells strawberries in large boxes and small boxes. 2 large boxes and 5 small boxes contain a total of 80 strawberries. 3 large boxes and 2 small boxes contain a total of 65 strawberries. How many strawberries are in each large box?

Solve the following system of linear equations for \(x\) and \(y\):
\(y = 3x\)
\(x + y = 12\)

Solve the following system of linear equations for \(x\) and \(y\):
\(\frac{x}{3} + \frac{y}{2} = 5\)
\(x - y = 5\)

Solve the following system of equations for \(x\) and \(y\):

\( \frac{1}{x} + \frac{1}{y} = \frac{5}{6} \)

\( \frac{3}{x} - \frac{2}{y} = \frac{1}{6} \)

A delivery truck carries two types of packages: Type A and Type B. It is known that:

2 packages of Type A and 5 packages of Type B weigh a total of \(24\) kg.
2 packages of Type A and 3 packages of Type B weigh a total of \(16\) kg.

(a) Let \(x\) kg be the weight of a Type A package and \(y\) kg be the weight of a Type B package. Form a pair of simultaneous linear equations to represent the information above.
(b) By solving the equations in (a), find the weight of one Type A package and one Type B package.

In a farm, there are some chickens and rabbits. Let the number of chickens be \(x\) and the number of rabbits be \(y\). It is known that:

(i) The total number of animals is 35.
(ii) The total number of legs is 94.

(a) Form a pair of simultaneous linear equations in \(x\) and \(y\) to represent the above information.
(b) Solve the simultaneous equations to find the number of chickens and the number of rabbits in the farm.
(c) If a new rabbit is added to the farm, find the new ratio of the number of chickens to the number of rabbits.