please help

Question

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

Answer 1

 

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)