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How do I solve this using substitution

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3 Answers

Solve using substitution
-4x + 3y = -24
-5x + y = -19
  • Start by rearranging one of the equations in terms of a variable
  • Lets choose the bottom equation and solve for y
-5x + y = -19
  • Add 5x to both sides
-5x + y + 5x = -19 + 5x
y = 5x - 19
  • Now replace y in the top equation with 5x - 19
-4x + 3y = -24
-4x + 3(5x - 19) = -24
  • Distribute the 3 across the parentheses
-4x + 15x - 57 = -24
  • Combine like terms then add 57 to both sides
11x - 57 = -24
11x - 57 + 57 = -24 + 57
11x = 33
  • Now divide both sides by 11
11x/11 = 33/11
x = 3
  • Finally, we can substitute our value for x in the bottom equation
y = 5x - 19
y = 5(3) - 19
y = 15 - 19
y = -4
 
x = 3, y = -4
-4X + 3Y = -24
-5x  + Y = -19
 
 Let's solve for Y in terms of X from the 2nd equation:
 
     Y = 5x -19
   
  Plug in the Y in 1st equation:
   
       - 4X + 3( 5X - 19) = -24
 
         -4X + 15X - 57 = -24
 
            11 X = 57 -24 = 33    X = 3
          
      Plug in X into 1st equation:
      -4(3) +3Y = -24
        3Y = -24 + 12 = -12      Y = -12 /3 = -4        Y= -4
                                                  
Hi Lindsay;
-4x+3y=-24
-5x+y=-19
Let's isolate one variable.
The second equation is easier.
-5x+y=-19
Let's add 5x to both sides...
5x-5x+y=5x-19
y=5x-19
Let's plug this into the first equation...
-4x+3y=-24
-4x+[(3)(5x-19)]=-24
Let's distribute the 3 within the brackets...
-4x+(15x-57)=-24
-4x+15x-57=-24
Let's combine like terms...
11x-57=-24
Let's add 57 to both sides...
57+11x-57=-24+57
11x=33
Let's divide both sides by 11...
(11x)/11=33/11
x=3
Let's plug this into either equation to establish y.  I randomly select the first...
-4x+3y=-24
[(-4)(3)]+3y=-24
-12+3y=-24
3y=-12
y=-4
Let's plug both values into the second equation to verify...
-5x+y=-19
[(-5)(3)]+(-4)=-19
-15-4=-19
-19=-19
It works!