This document provides instruction on solving simultaneous equations. It defines simultaneous equations as involving two or more mathematical equations worked with together. The steps provided are to 1) label the equations, 2) substitute one equation into the other to form a third equation, 3) solve the third equation for the variable, and 4) write down the final values of the variables. An example is worked through demonstrating these steps to solve the simultaneous equations y - x = 2 and x - 3y = 1 for values of x and y. Practice problems are provided for students to work through.

1. 1
simultaneos equations
Grade 10
09 may 2013
by MR HG HLUNGWANI 201122395

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x - 3(x + 2) = 1 ( y has been replaced by "x + 2" )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!!!