Maths
Maths, Physics Revision
HOME
Physicss Physics A Level Physics Home Revision hut
Simultaneous Equations
1,Solving simultaneous equations using the graphical method
Take the two equations 2x + 2y =10 and 4x - 2y = 8 consider equation 2x + 2y =10 when x = 0, 2y = 10, so y = 5 the line crosses the Y axis at y=5 when y = 0, 2x = 10, so x=5 the line crosses the X axis at x = 5
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 values of x and y are
 where the lines cross
Play the animation
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
2,Solving simultaneous equations using the elimination method Look at these two equations (1) 4x + y = 11 And (2) 2x + y = 7 Subtract equation (2) from equation (1) 2x + 0 = 4 2x = 4 x= 2
Substitute this value back into equation (1)
4 + y = 11 y =3 Check answer in equation (2)
4 + 3 =7  Correct
If one of the unknowns have different signs (1) 4x - y = 4 (2) x + y =6
This time add equation (1)
to equation (2)
5x +0 = 10 x = 2 (-y +y = 0) Substitute this value back into equation (1) 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
(1) 2x +y = 8 (2) x + 2y = 7 Multiply equation (1) by 2 (3) 4x + 2y = 16 Subtract (2) from (3) 3x + 0 =9 x= 3
Substitute in equation (1)
6 + y = 8 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 (2) 2x + 3y = 14
Multiply (1) by 3
(3) 12x + 6y = 60
Multiply (2) by 2
(4)     4x + 6y =  28
Subtract (4) from (3)
8x + 0 = 32
 x = 4
Substitute in equation 1
16 + 2y = 20
 y = 2
Check answer in (2)
8 + 6 = 14 correct
So x = 4, y = 2
And different signs
(1) 2x + 3y = 16 (2) 3x - 4y = 7 Multiply (1) by 4
(3)     8x + 12y = 64
Multiply (2) by 3
(4) 9x -12y = 21 Add (3) and (4)
17x +0 = 85
 x= 5
Substitute in (1) 10 + 3y = 16 y = 2 Check answer in (2)
15 - 8 = 7  correct
So x= 5, y = 2 Solving by elimination Click here for
top
Take a test