二次方程 AND simultaneous EQUATIONS（联立方程）

worked example

Solve the following equations simultaneously.

x + y = 5

2x - y = 4

Solution

You will remember from your earlier work on coordinate geometry that, when the solutions to

an equation such as x + y = 5 are graphed on a number plane, they form a straight line.

Hence, to solve the equations x + y = 5 and 2x − y = 4

simultaneously, we could simply graph each line and

find the point of intersection. Since this point lies on

both lines, its coordinates give the solution.

• The lines x + y = 5 and 2x − y = 4 intersect at (3, 2).

Therefore the solution is:

x = 3

y = 2

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