Where do the graphs of linear equations 2x+3y=4 and 5x+6y=7 intersect

5x + 6y = 7                         SUBSTITUTION METHOD
2x + 2y = 4 

         5x + 6y = 7                      Solve for either x or y in 1 of the 2 equations.
               - 6y - 6y
     
         5x = -6y + 7 
           
          5       5      5

          x = -6/5y + 7/5

2(-6/5y + 7/5) + 2y = 4             Substitute the expression you got for x or y into 
-12/5y + 14/5 + 2y = 4              the other equation.
-2/5y + 14/5 = 4 
          - 14/5  - 14/5 

-2/5y = 6/5 
 
- 2/5y  - 2/5y

y = -3 

5x + 6(-3) = 7                             Plug in the value you got for y in step 2 into the 
5x - 18 = 7                                  equation that you didn't use.
    + 18 + 18

5x = 25 
---    
5       5

x = 5 

(x,y) ⇒ coordinate
(5,-3) ⇒ final answer