2. 2
Lesson outcomes
• At the end, learners should be able to:
• Label their given equations as 1 and 2 for them
to formulate equation 3
• They should be able to use their labelled
equations for substituition and solving.
• They should be able to work with the real life
examples.
3. 3
def: Simultaneous equations- a
situation whereby you work with two
or more mathematical equations.
Example: solve for x and y
simultaneously.
simultaneous equations
4. 4
StepS
Label your equations as 1 and 2.
Substitute one of the equations(1 or 2)
to formulate equation 3.
Solve for x or y.
write down the final values of y and x.
5. 5
1.solve for x and y simultaneously
y - x = 2
x - 3y = 1
solution
step 1-Label your equations as 1 and 2.
y - x = 2.......................1
x - 3y = 1......................2
exampleS
6. 6
Solution continueS......
Step 2-Substitute one of the
equations(1 or 2) to formulate
equation 3.
From equation no.1 "y = x + 2"........3
Substitute equation 3 into equation 2,
therefore,
7. 7
Solution continueS.....
step 3-Solve for x or y.
x - 3(x + 2) = 1 ( y has been replaced by "x + 2" )
x - 3x - 6 = 1 ( solve for x )
x - 3x - 6 - 1 = 0 (Rearrange your equation and
take your 1 to the LHS)
8. 8
Solution continueS.........
x - 3x - 6 - 1 = 0
-2x - 7 = 0 (simplify your equation)
-2x = 7 ( take 7 to your RHS)
x = 7/-2 (divide both sides by -2)
9. 9
Solution continueS.........
step 4-write down the final values of y and x.
for x =7/-2 :
y : y - (7/-2) = 2 (substitute x at equation 1 to
find the value y)
y+7/2 = 2 (solve for y )
y = 2 - 7/2
y = -3/2
Therefore x = 7/-2 and y = -3/2
10. 10
practise for exam questions
solve for x and y simultaneously :
1. 2x + y = 4x + 1
4x + 2y = 12
2. 4x + 8y = 16
y + 15x = 9
3. 3x + 24y = -1
y + 6x = 8x + 2
Good
luck!!!