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0=24-9y+x -10y=-9x-26 solve by elimination

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2 Answers

Solve by elimination
0 = 24 - 9y + x
-10y = -9x - 26
  • First we have to choose which variable to eliminate;
    let's eliminate x
  • Then we should rearrange both equations so y is on the left side
9y = x + 24
-10y = -9x - 26
  • In order to eliminate x the x term in the top equation added to the x term in the bottom equation must equal zero. This is called the additive inverse.
  • To do this we can multiply the entire top equation by 9.
9(9y = x + 24)
81y = 9x + 216
  • Now we combine the top equation with the bottom equation
 81y =  9x + 216
-10y = -9x   - 26
 71y =  0x + 190
  • Next we divide both sides by 71 to solve for 7
71y = 190
71y/71 = 190/71
y = 190/71
  • Now we can substitute our y value into the top equation to solve for x
0 = 24 - 9y + x
0 = 24 - 9(190/71) + x
0 = 24 - 1710/71 + x
  • Multiply 24 by 71/71 so we can combine like terms
0 = 24(71/71) - 1710/71 + x
0 = 1704/71 - 1710/71 + x
0 = -6/71 + x
  • Finally, we add 6/71 to each side to solve for x
0 + 6/71 = -6/71 + x + 6/71
x = 6/71
  • With this problem we should check our answers with both equations
 
0 = 24 - 9y + x
0 = 24(71/71) - 9(190/71) + 6/71
0 = 1704/71 - 1710/71 + 6/71
0 = -6/71 + 6/71
0 = 0
 
-10y = -9x - 26
-10(190/71) = -9(6/71) - 26(71/71)
-1900/71 = -54/71 - 1846/71
-1900/71 = -1900/71
 
 
x = 6/71   y = 190/71
 
 Just separate numbers.
 
0 = 24 +9y + x
 
-10 Y = -9x -26
 
 
    9(X - 9y = = -24)
      -9x +10Y = 26         
       -71 Y = 9( -24) + 26
 
         Y = 190/71
        
         X = 9y -24 = 6/71

Comments

Check your work, those values of x and y don't work with 0 = 24 + 9y + x