How to Solve Simultaneous Equations Graphically

Step-by-Step Guide

1. 1

   Step 1: Write your 2 equations clearly.

   Write your 2 equations in an organised, clear way.
   
   This will make it easier later.
   
   In this guide, we are going to use equations 3x+4y=22 and x+2y=2 as an example.
2. 2

   Step 2: In the first equation

   Replace x with 0, and solve the equation.
   
   This should give you the value of y.
   
   Using the example before: 3*0+4y=22, which becomes 4y=22, and then y=5½ You now have your first coordinate, (0 ; 5½) , In the first equation, let y be 0 and solve the equation.
   
   This will give you the value of x.
   
   Using the example: 3x+4*0=22 which becomes 3x=22 which gives us the answer of x=7⅓ You now have a set of coordinates for your first line, (0 ; 5½) and (7⅓ ; 0) , Draw the line of your first equation on it. , Then solve the equation, giving you the value of y.
   
   Using the example, it's 0+2y=2, which becomes 2y=2 and y=1 First coordinate is now (0 ; 1) , Solve the equation and get the value of x.
   
   Example: x+2*0=2, which becomes x=2.
   
   Second coordinate is now (2 ; 0) , If needed, increase the length of the 2 lines until they meet. , Get it's coordinates (x ; y).
   
   The x coordinate will be the value of x in the equation, and the y coordinate will be the value of y! If you've been using the example, the lines should meet at point (18 ;
   -8). x will be 18, and y will be
   -8!
3. 3

   Step 3: let x be 0.

4. 4

   Step 4: Let y be 0.

5. 5

   Step 5: Draw a graph with 4 quadrants.

6. 6

   Step 6: In the second equation

7. 7

   Step 7: let x be 0.

8. 8

   Step 8: Let y be 0.

9. 9

   Step 9: Draw the line of the second equation on the same graph as before.

10. 10

    Step 10: Look at the point in which the 2 lines meet.

Detailed Guide

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