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Understanding Simultaneous Equations: Step-by-Step Guide to Solve Them

Simultaneous equations can be solved when two equations share common variables, allowing for specific solutions. For example, in the equations x + y = 5 and x - y = 1, the values of x and y that satisfy both equations are x = 3 and y = 2. This guide explains effective methods to solve simultaneous equations, including addition and subtraction techniques based on whether the middle signs of the equations are the same or different. Join us as we break down various examples and improve your problem-solving skills!

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Understanding Simultaneous Equations: Step-by-Step Guide to Solve Them

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  1. 4 January, 2020 Simultaneous Equations Let me explain. If you have an equation like: x + y = 5, there are lots of answers. What are simultaneous equations

  2. Here are some of these answers I can think of some more because 1.5 + 3.5 = 5 so x = 1.5 and y = 3.5 etc.

  3. There are lots of answers that fit the equation x + y = 5 That’s right but suppose that we have another equation to go with x + y = 5 and the x and y must be the same numbers for both equations. x + y = 5 x – y = 1 Like this

  4. x + y = 5 x – y = 1 The only values that will fit both equations are x = 3 and y = 2. Equations like this are called simultaneous equations. 3 + 2 = 5 3 – 2 = 1

  5. Here is a method for solving simultaneous equations x +y=9 x –y= 5 • Make sure that the middles are the same • y • y

  6. Here is a method for solving simultaneous equations x +y=9 x –y= 5 • Make sure that the middles are the same • If the signs are different ADD • (+ y) and (– y) have different signs so ADD

  7. Here is a method for solving simultaneous equations x +y=9 x –y= 5 2x= 14 • Make sure that the middles are the same • If the signs are different ADD • x+x=2x and (+ y ) + (- y ) = 0 • and 9 + 5 = 14

  8. Here is a method for solving simultaneous equations x +y=9 x –y= 5 2x= 14 x =7 • Make sure that the middles are the same • If the signs are different ADD • Find the value of x • 2 x = 14 • x = 14 ÷ 2 • x = 7

  9. Here is a method for solving simultaneous equations x +y=9 x –y= 5 2x= 14 x =7 x +y=9 7+y=9 y = 9 – 7 y =2 • Make sure that the middles are the same • If the signs are different ADD • Find the value of x • Use this to find the value ofy • 7 + y = 9 • y = 9 – 7 • y = 2

  10. Here is another pair of simultaneous equations 2x +y=11 x –y= 4 To solve, follow the steps

  11. 2x +y=11 x –y= 4 3x= 15 • Make sure that the middles are the same • If the signs are different ADD • 2x + x = 3x • (+y) + (–y) = 0 • 11 + 4 = 15

  12. 2x +y=11 x –y= 4 3x= 15 x =5 • Make sure that the middles are the same • If the signs are different ADD • Find the value of x • 3x= 15 • x =15 ÷ 3 • x = 5

  13. 2x +y=11 x –y= 4 3x= 15 x =5 2x + y= 11 10 +y= 11 • Make sure that the middles are the same • If the signs are different ADD • Find the value of x • Use this to find the value ofy

  14. 2x +y=11 x –y= 4 3x = 15 x =5 2x + y= 11 10 +y= 11 y = 11 – 10 y = 1 • Make sure that the middles are the same • If the signs are different ADD • Find the value of x • Use this to find the value ofy

  15. When the middle signs are the same 2x + y = 14 x + y = 4 The same

  16. 2x +y=14 x +y= 9 x= 5 2x + y= 14 10 +y= 14 y = 14 – 10 y = 4 • Make sure that the middles are the same • If the signs are the same SUBTRACT • Find the value of x • Use this to find the value ofy

  17. Make sure that the middles are the same • If the signs are the Same SUBTRACT • If the signs are Different ADD • 3. Find the value of x • 4. Use this to find the value ofy

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