Simultaneous equations
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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.
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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.