Michael V. | Great Tutor in Multiple SubjectsGreat Tutor in Multiple Subjects

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

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