F.2 maths(linear equations in two unknowns)

1. Using the method of substitution , solve the simultaneous equations
3x-2y=12........................(1)
2x+y=1...........................(2)
Solution : From (2), we have y=____________............(3)
Substitute (3) into (1)
3x-2( _______ )=12
3x-_________=12
________x=______
x=______
Substitute: x=______ into (3)
y=_______
=_______
∴The solution is x=_______and y=______

2. Using the method of substitution , solve the simultaneous equations
2x-5y=15...................(1)
3x+y=14....................(2)

(1)×3 __________=_________.........(3)
(2)×2 __________=_________.........(4)
(4)-(3)__________=_________
y=_________
substitute y=________ into(2)
___________=___________
x=___________
∴The solution is x=_______and y=_______

3. the sum of two numbers is 143 and their difference is 9.Find these two
numbers. let the large number be x, the small number be y.
Equations:___________............(1)
___________............(2)

4.Simultaneous linear equations in teo unknowns have only one solution?
Try to solve the simultaneous linear equations
2x-3y=7..............(1)
4x-6y=14............(2)
what is the result?

What do you discover?

What is the relationship between these two equations?