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

Question

solve each system by elimination

Answer 1

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

 

Answer 2

 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