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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