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The graph shows the lines 5x+4y=7 and x-3y=9. Based on the graph, estimate the solution of the system of equations:
 
5x+4y=7
x-3y=9

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You do not present the graph.
 

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Tim E. | High School and M.S. Math, Physics tutor - ret. Aerospace EngrHigh School and M.S. Math, Physics tutor...
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1st equation in slope intercept form is:  y =  (-5/4)X + 7/4
2nd equation                                         y =  (1/3)X -  3 
 
A graph would show them intersecting in the 4th quadrant. 
 
to solve the two equations:
 
 5X  + 4Y = 7
   X  -  3Y = 9
 
mult 2nd eqn by -5 and add the two eqn to elim X
 
  5X  +  4Y  =   7
 -5X  + 15Y = -45
-----------------------
  0X  + 19Y = -38      so   Y = -38/19   or   Y = -2  <----
 
 subst Y = -2  in either eqn,  I'll do the 2nd eqn,  to find X
 
   X - 3(-2) = 9    or   X + 6 = 9   or  X = 3  <----
 
 so the solution, which is the intersection point of the 2 lines is at (3,-2)