Solve: `-24-8x=12y`  and `1+ (5/9)y=(-7/18)x` solving systems using elmination  24-8x=12y and 1+5/9y=-7/18x

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to move the terms of the first and second equations, terms that contain x and y, to the left side, such that:

`{(-8x - 12y = 24),(7/18 x + 5/9 y = -1):}`

You need to bring the terms to the second equation to a common denominator, such that:

`{(-8x - 12y = 24),(7x + 10y = -18):}`

 You need to eliminate the variable x, hence, you need to multiply by 7 the first equation and you need to multiply by 8 the second equation, such that:

`{(-56x - 84y = 168),(56x + 80y = -144):}`

Adding the equations yields:

`-4y = 24 => y = -6`

Substituting -6 for y in equation 7x + 10y = -18 yields:

`7x - 60= -18 => 7x = 60 - 18 => 7x = 42 => x = 6`

Hence, evaluating the solution to the system of equations, using elimination, yields `x` `= 6`  and `y = -6` .

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