How do you solve the following system: $- 29 = 5 y - 3 x, 5 x + 2 y = 12$ $-29=5y-3x, 5x+2y=12$ ?

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How do you solve the following system: $- 29 = 5 y - 3 x, 5 x + 2 y = 12$ $-29=5y-3x, 5x+2y=12$ ?

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Answer 1 · 2018-03-22T01:02:36

$x = \frac{118}{31}$ $x = 118/31$ and $y = - \frac{109}{31}$ $y = -109/31$

Explanation:

We can eliminate a variable by subtracting out an equation.

For example, let's take 3 times the second plus five times the first:

$3 (5 x + 2 y = 12) \Rightarrow 15 x + 6 y = 36$ $3(5x+2y = 12) implies 15x + 6y = 36$
$5 (- 3 x + 5 y = - 29) \Rightarrow - 15 x + 25 y = - 145$ $5(-3x + 5y = -29) implies -15x + 25y = -145$
Adding them together,
$31 y = - 109 \Rightarrow y = \frac{- 109}{31}$ $31y = -109 implies y = (-109)/31$

We can now plug this into our second equation from before and get $x$ $x$ :
$5 x + 2 (\frac{- 109}{31}) = 12 \Rightarrow 5 x = 12 + \frac{218}{31} = \frac{590}{31}$ $5x + 2((-109)/31) = 12 implies 5x = 12 + 218/31 = 590/31$
$x = \frac{118}{31}$ $x = 118/31$

Thus we have our answer.

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How do you solve the following system: $- 29 = 5 y - 3 x, 5 x + 2 y = 12$ $-29=5y-3x, 5x+2y=12$ ?

1 Answer

Explanation:

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Math

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How do you solve the following system: −29=5y−3x,5x+2y=12-29=5y-3x, 5x+2y=12 ?

1 Answer

Explanation:

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How do you solve the following system: $- 29 = 5 y - 3 x, 5 x + 2 y = 12$ $-29=5y-3x, 5x+2y=12$ ?