This document explains how to solve simultaneous equations using an example with the total number of boys and girls in two locations. It shows forming two equations: one with the total of boys and girls equaling 156, and another relating the number of girls in one location to the number of boys in the other. It substitutes one equation into the other to solve for the individual values of boys and girls. The key steps are forming equations from the information given, substituting one equation into the other, and solving to find the individual values requested.

1. Simultaneous equations

2. Using 2 symbols to represent 2
values
 Here there are a few different values we
can use, namely number of boys/girls in
playground, number of boys/girls in
library, total number of pupils etc
 However, if we take a closer look at it,
using the total number of boys and girls
in the two places
 This is because the question tells us
their total is156, making the first equation
very easy to form

3. Forming the simultaneous
equations
 So, Let A be the total number of
boys and B be the total number of
girls
 The first equation is easy to get. It is:
A+B=156(stated in the qurstion)

4. Forming the simultaneous
equations
 The second equation is also given in
the question, but it is harder to find.
 It is B-15(number of girls in
playground)= A-56(number of boys
in library)+17(because there’s more
girls than boys)

5. Solving
 From the first equation, we can get the
following value for A:
A=156-B
Let’s call this the third
equation(because this is the one we
will be substituting)

6. Substituting
 Now, we have to substitute the third
equation into the second equation(we
can do so because the value of A in
both equations are the same)
 B-15= 156-B-56+17

7. Solving
 Now if we add up some numbers and
move them around..
 B-15=117-B
 2B=132
 B=66

8. Solving
 Now that we know B, we can substitute
that value into any one of the equations
A+B=156
A+66=156
A=90
Thus total number of boys is 90 and
total number of girls in 66

9. Conclusion
 That is what simultaneous equation is
about
 You basically form 2 equations and
substitute one into the other
 The hard part is knowing which values
to use in your equations, so for
beginners, I recommend using values
which forms equations easily found in
the question, or simply use the values
the question is asking for.