How do you solve the following system?: $4x -12y =-3 , -3x +y = 18$

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Answer 1 · 2017-01-15T15:02:32

See entire solution process below:

Step 1) Solve the second equation for $y$ :

$-3x + y = 18$

$-3x + color(red)(3x) + y = 18 + color(red)(3x)$

$0 + y = 18 + 3x$

$y = 3x + 18$

Step 2) Substitute $3x + 18$ for $y$ in the first equation and solve for $x$ :

$4x - 12y = -3$

$4x - 12(3x + 18) = -3$

$4x - 36x - 216 = -3$

$-32x - 216 = -3$

$-32x - 216 + color(red)(216) = -3+ color(red)(216)$

$-32x - 0 = 213$

$-32x = 213$

$(-32x)/color(red)(-32) = 213/color(red)(-32)$

$(color(red)(cancel(color(black)(-32)))x)/cancel(color(red)(-32)) = -6.65625$

$x = -6.65625$

Step 3) Substitute $-6.65625$ for $x$ into the solution for $y$ in the second equation in Step 1 and calculate $y$ :

$y = 3x + 18$

$y = (3 xx -6.65625) + 18$

$y = -19.96875 + 18$

$y = -1.96875$

The solution is: $x = -6.65625$ and $y = -1.96875$

How do you solve the following system?: 4x -12y =-3 , -3x +y = 184x -12y =-3 , -3x +y = 18