How do you solve the following system?: $17 x + 19 y = 14, - 7 x + 15 y = - 22$ $17x +19y =14, -7x +15y = -22$

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Answer 1 · 2017-10-27T21:42:15

$y = - 0.71$ $y = -0.71$
$x = 1.62$ $x = 1.62$

$17 x + 19 y = 14$ $17x+19y=14$
$- 7 x + 15 y = - 22$ $-7x+15y=-22$

Using one of the equations, make either $x$ $x$ or $y$ $y$ the subject.

$17 x + 19 y = 14 \to 17 x = 14 - 19 y$ $17x+19y=14 -> 17x = 14-19y$

$x = \frac{14 - 19 y}{17}$ $x = (14-19y)/17$

Then inject this in place of the $x$ $x$ in the second equation to calculate $y$ $y$ .

$- 7 (\frac{14 - 19 y}{17}) + 15 y = - 22$ $-7((14-19y)/17) +15y = -22$

Multiply out the bracket.

$\frac{- 98 + 133 y}{17} + 15 y = - 22$ $(-98+133y)/17 + 15y = -22$

Multiply everything by $17$ $17$ to get rid of fractions.

$- 98 + 133 y + 255 y = - 374$ $-98 + 133y +255y = -374$

Now calculate $y$ $y$ .

$388 y = - 276$ $388y = -276$

$y = - \frac{276}{388}$ $y = -276/388$

$y = - 0.71$ $y = -0.71$

Now substitute the calculated $y$ $y$ value into the rearranged equation to calculate $x$ $x$ .

$x = \frac{14 - 19 (- 0.71)}{17}$ $x = (14-19(-0.71))/17$

$x = 1.62$ $x = 1.62$

How do you solve the following system?: 17x+19y=14,−7x+15y=−2217x +19y =14, -7x +15y = -22