Simultaneous Equations
1,Solving simultaneous equations using the graphical method
consider equation 4x - 2y = 8
when x =0, - 2y = 8, so y = - 4
the line crosses the Y axis at y = - 4
when y = 0, 4x = 8, x=2
the line crosses the X axis at x=2
the line crosses the X axis at x=2
The values of x and y are
where the lines cross
where the lines cross
Simultaneous equations are two equations both with two unknowns in them. You cannot
find the unknowns using one equation, you have to use them both. You can use either
of the following methods
find the unknowns using one equation, you have to use them both. You can use either
of the following methods
2x + 0 = 4
2x = 4
x= 2
2x = 4
x= 2
4 + y = 11
y =3
y =3
4 + 3 =7 Correct
If one of the unknowns have different signs
(1) 4x - y = 4
(2) x + y =6
(-y +y = 0)
8 - y = 4
y = 4
Check the answer in equation (2)
2 + 4 =6 correct
So x = 2 and y = 3
So x = 2 and y = 4
If the unknowns have different values
Substitute in equation (1)
6 + y = 8
y=2
y=2
Check the answer in (2)
3 + 4 = 7 correct
So x = 3, y = 2
Sometimes you need to multiply both equations
(1) 4x + 2y = 20
Multiply (1) by 3
(3) 12x + 6y = 60
(4) 4x + 6y = 28
8x + 0 = 32
x = 4
x = 4
Substitute in equation 1
16 + 2y = 20
y = 2
y = 2
8 + 6 = 14 correct
So x = 4, y = 2
And different signs
(1) 2x + 3y = 16
(3) 8x + 12y = 64
Multiply (2) by 3
(4) 9x -12y = 21
Add (3) and (4)
17x +0 = 85
x= 5
x= 5
Substitute in (1)
Check answer in (2)
15 - 8 = 7 correct
So x= 5, y = 2
Solving by
elimination
elimination
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