How do you solve the following system?: $3 x - 9 y = - 13, - 2 x + 17 y = 8$ $3x -9y =-13 , -2x +17y = 8$

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How do you solve the following system?: $3 x - 9 y = - 13, - 2 x + 17 y = 8$ $3x -9y =-13 , -2x +17y = 8$

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Answer 1 · 2016-04-29T22:47:47

$x = - \frac{139}{69}$ $x=-139/69$
$y = \frac{50}{69}$ $y = 50/69$

Explanation:

$3 x - 9 y = - 13$ $3x-9y = -13$ and
$- 2 x + 17 y = 8$ $-2x+17y = 8$

multiply first statement by "2" and the second statement by "3" to get to a common coefficient of 'x'
$2 (3 x - 9 y) = 2 (- 13)$ $2(3x-9y) = 2(-13)$
$3 (2 x + 17 y) = 3 (8)$ $3(2x+17y) = 3(8)$

$6 x - 18 y = - 26$ $6x-18y = -26$
$6 x + 51 y = 24$ $6x+51y = 24$

then, subtract second statement from first statement
$- 69 y = - 50$ $-69y = -50$

now that y is isolated, we know that
$y = \frac{50}{69}$ $y = 50/69$

to solve for x, substitute the value for 'y' into one of the statements

$3 x - 9 (\frac{50}{69}) = - 13$ $3x-9(50/69) = -13$

divide the statement by 3
$x - 3 (\frac{50}{69}) = - \frac{13}{3}$ $x-3(50/69)=-13/3$
$x - (\frac{50}{23}) = - \frac{13}{3}$ $x-(50/23)=-13/3$
$x = - \frac{13}{3} + \frac{50}{23}$ $x=-13/3 +50/23$

lastly, solve for lowest common denominator
$x = \frac{- 299 + 150}{69} = - \frac{139}{69}$ $x=(-299 + 150)/69=-139/69$

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How do you solve the following system?: $3 x - 9 y = - 13, - 2 x + 17 y = 8$ $3x -9y =-13 , -2x +17y = 8$

1 Answer

Explanation:

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How do you solve the following system?: $3 x - 9 y = - 13, - 2 x + 17 y = 8$ $3x -9y =-13 , -2x +17y = 8$