Solving simultaneous equations graphically

Example

Solve the following pair of equations by drawing graphs:-
   x + y = 6
   x  - y = -4
  
    Solution

• Re-arrange equations into form y = mx + c

              y = 6 - x
              y = x + 4

• Take first equation.             

Pick 3 sensible points for x, then solve for y.
 To do this, substitute the value for x into the equation:

eg, when x = -2, y= 6 -(-2) = 8

Tip: Always include x = 0

 

Plot co-ords ( -2,8), (0,6) , (6, 0)
Join with straight line.

 

• Repeat for other equation.

 

      Plot Co-ords ( -4,0), (0,4) , (4, 8)  and join with straight line.

 

        

 

• Read off intersection. ( 1,5)

         so  x = 1,  y = 5
            Check  
             x + y = 6,so 1+5 = 6   ü
               x-y = - 4, 1-5 = - 4 ü

• Write out solution    

The solution is the point of intersection  ( 1, 5)
 x = 1,  y = 5

Solving algebraically