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Linear Combination: How to:
    2x + 3y = 7
    3x + 4y = 10

   3(2x + 3y = 7)
+-2(3x + 4y = 10)

      6x + 9y = 21
    -6x - 8y = -20
              y = -1

 2x + 3(-1) =7
    2x - 3 = 7
         +3 =+3
      2x = 10
       2      2
         x = 2

Answer: (2,1)

 Multiply both equations to eliminate the varible 
Add both the equations together
Solve for y
 

Plug in y into one orignal problem
Solve for x
 
                                                                                          
 
Substitution: How to:
      3x - 4y = -15
      5x + y = -2

y = -5x - 2
 

3x - 4(-5x - 2) = -15>
  3x + 20x + 8 = -15
                 -8     -8
       23x = -23
         23       23
             x = -1

Answer: (-1,3)
 
 

Solve for Y
Substitute -5x-2 for y and solve
for x
 

Substitute -1 in one of the original problems and solve for y to find the point of intersection
                                                                                        
Word Problem: Using Linear Combination:
      The sum of a certain number and a 2nd number is -42.  The first number minus the 2nd number is 52.  Find the number.

      x + y = - 42
    + x - y = 52
       2x = 10
        2      2
           x = 5
 
       5 + y = - 42
     - 5      ;    - 5
            y = - 47

Answer: (5,- 47)
 
 

Convert word problem into an algebra problem
Add problems together
Sovle for x
 

Plug in x in one of the origimal problems
Solve for y
 
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