Elimination method.
Solving simultaneous equations by elimination method.
3x - 2y = 11
2x - 2y = 10
Method
Let 3x - 2y = 11 be equation (i
and 2x - 2y = 10 be equation (ii)
Substract equation (ii) from equation (i)
3x - 2y = 11
- 2x - 2y =10
x = 1
The Value of x is now equal to 1. In equation (i) or (ii) substitute 1 for x.
Take3x - 2y = 11
3x1 - 2y = 11
3 - 2y = 11
3 - 3 - 2y = 11 - 3
-2y = 9
-2y = 8
The values of x and y that satisfies both simultaneous linear equations are
x = 1 and y = -4.
Solve the simultaneous equation
2x - 4y = 2
12x + 4y = 40
Let 2x - 4y = 2 be equation (i)
and 12x + 4y = 40 be equation (ii)
Add equation (i) to equation (ii)
2x - 4y = 2
+ 12x + 4y = 40
14x = 42
Solve this linear equation by dividing both sides of the equation by 14.
14x = 42 14 14
x =3
The value of x is 3.
In equation (i) and (ii) substitute 3 for x.
Take 2x - 4y = 2
2x3 - 4y = 2
4 - 4y = 2
5 - 6 - 4y = 2 -6
-4y = -4 -4 -4
y = 1
The values of x and y that satisfies both simultaneous linear equations
are x = 3 and y = 1
In the above two illustrations, it was easy to eliminate one unknown
for its coefficients were numerically equal. When the signs infront of the
unknown to be eliminated are the same we subtract, and when the signs
are different we add.
Solve the simultaneous equations.
9x + 3y = 21
3x - 6y = 0
Let 9x + 3y = 21 be equation (i)
and 3x - 6y =0 be equation (ii)
Note the coefficients of the unknowns are not the same.
Multiply equation (ii) by 3 to make the coefficients of x equal numerically.
(3x - 6y = 0) x3
9x - 18y = 0
Let this equation be equation (iii)
9x - 18y = 0 ----------(iii)
Subtract equation (iii) from equation (i) to eliminate x.
9x + 3y = 21 --------(i)
9x - 18y = 0 ---------(ii)
21y = 21
Dividing both sides by 21
21y = 21 21 21
y = 1
In equations (i), (ii) or (iii) substitute 1 for y.
9x + 3y = 21
9x + 3 x 1 = 21
9x + 3 = 21
9x + 3 - 3 = 21 – 3
9x = 18
9x = 18 9 9
x = 2
The values of x and y that satisfies the equations are x = 2 and y = 1
Solve the simultaneous linear equations
5x + 4y = 17
3x + 3y = 12
Let 5x + 4y = 17 be equation (i)
and 3x + 3y = 12 be equation (ii)
5x + 4y = 17 --------- (i)
3x + 3y = 12 --------- (ii)
Multiply equation (i) by 3 and equation (ii) by 5, so as to make
the coefficients of x equal numerically.
3 (5x + 4y = 17)
15x + 12y = 51. Let this be equation (iii)
and 5(3x + 3y = 12)
15x + 15y = 60. Let this be equation (iv)
Subtract equation (iv) form equatiom (iii) to eliminate x now that its
coefficients are numerically equal in both equations.
15x + 12y = 51----------(iii)
- 15x + 15y = 60 ---------- (iv)
-3y = -9
-3y = -9 -3 -3
y = 3
In either equations (i), (ii), (iii) or (iv) substitute 3 for y to solve for x.
Taking 3x + 3y = 12
3x + 3(3) = 12
3x + 9 = 13
3x + 9 - 9 = 12 – 9
3x = 3
x = 1
Note in solving the simultaneous equation above, that is
15x + 12y = 51----------(iii)
- 15x + 15y = 60 ---------- (iv)
Multiply equation (i) by 3 and equation (ii) by 4 to make the coefficients
of y equal numerically.
3(5x + 4y = 17)
4(4x + 3y = 12)
15x + 12y = 51 Let this be equation (iii)
12x + 12y = 48. Let this be equation (iv)
When solving simultaneous equations by eliminations method.
Decide which variable to eliminate.
Make the coefficient of the variable the same in both equations.
Eliminate the variable by addition or subtraction as is appropriate.
Solve for the remaining variable
Substitute your value for part (4) above in any of the original equations
to solve for the other variable.