Simultaneous linear equations：練習問題

Solve the following simultaneous linear equations:
\(x + y = 15\)
\(x - y = 3\)

Solve the following simultaneous linear equations:
\(2x + 3y = 13\)
\(5x - y = 7\)
Find the value of \(x + y\).

Two lines have equations \(y = ax + b\) and \(y = bx + a\).
They intersect at the point \((2, 5)\).

Work out the values of \(a\) and \(b\).

A rectangular field has a perimeter of \(40\) m. The length of the field is \(4\) m more than its width.

Find the dimensions of the field and determine its area.

Solve the following simultaneous linear equations to find the values of \(x\) and \(y\):

\(\frac{x}{2} + \frac{y}{3} = 7\)

\(\frac{x}{4} - \frac{y}{2} = -1\)

Solve the simultaneous linear equations:
\(5x + 2y = 11\)
\(4x - 3y = 18\)

The lines with equations \(y = ax + b\) and \(y = bx + a\) intersect at the point \((2, 5)\).
Work out the values of \(a\) and \(b\) by setting up and solving simultaneous linear equations.

Find the exact solution of the following simultaneous linear equations:
\(4x + 3y = 2\)
\(3x + 5y = -15\)

Solve the following simultaneous linear equations:
\(x + y = 14\)
\(x - y = 2\)

Find the values of \(x\) and \(y\).

At a cafe, 3 coffees and 2 teas cost \(\pounds 10.80\).
5 coffees and 4 teas cost \(\pounds 19.20\).

(a) Write down a pair of simultaneous linear equations to represent this information.

(b) Solve your equations to find the cost of one coffee and the cost of one tea.