solve each system by elimination

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

-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.

81y = 9x + 216

- Now we combine the top equation with the bottom equation

-10y = -9x - 26

71y = 0x + 190

- Next we divide both sides by 71 to solve for 7

71y/71 = 190/71

y = 190/71

- Now we can substitute our y value into the top equation to solve for x

0 = 24 - 9(190/71) + x

0 = 24 - 1710/71 + x

- Multiply 24 by 71/71 so we can combine like terms

0 = 1704/71 - 1710/71 + x

0 = -6/71 + x

- Finally, we add 6/71 to each side to solve for x

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

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