How do you solve the following system?: $16 x + 13 y = 7, - 19 x + 15 y = - 2$ $16x +13y =7, -19x +15y = -2$

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How do you solve the following system?: $16 x + 13 y = 7, - 19 x + 15 y = - 2$ $16x +13y =7, -19x +15y = -2$

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Answer 1 · 2018-04-25T12:13:20

$x = \frac{131}{7}$ $x = 131/7$

$y = - \frac{2047}{91}$ $y = -(2047)/91$

Explanation:

$16 x + 13 y = 7$ $16x+13y = 7$
$15 y - 19 x = - 2$ $15y - 19x =-2$

In equation 1, make $y$ $y$ the subject.

$13 y = 7 - 16 x \to y = \frac{7 - 16 x}{13}$ $13y = 7-16x -> y = (7-16x)/13$

Inject that into equation 2.

$15 (\frac{7 - 16 x}{13}) - 19 x = - 2$ $15((7-16x)/13) - 19x = -2$

Solve for $x$ $x$ .

$\frac{105 - 240 x}{13} - 19 x = - 2$ $(105-240x)/13 -19x = -2$

$\frac{105 - 240 x}{13} = 19 x - 2$ $(105-240x)/13 = 19x - 2$

$105 - 240 x = 247 x - 26$ $105 -240x = 247x - 26$

$247 x - 240 x = 105 + 26$ $247x-240x = 105+26$

$7 x = 131$ $7x = 131$

$x = \frac{131}{7}$ $x = 131/7$

Inject the value $x$ $x$ into the rearranged equation 1 to calculate the value of $y$ $y$ .

$y = \frac{7 - 16 (\frac{131}{7})}{13}$ $y = (7-16(131/7))/13$

$y = - \frac{2047}{91}$ $y = -(2047)/91$

Answer 2 · 2018-04-25T12:14:19

$x = \frac{131}{487}$ $x=131/487$
$y = \frac{101}{487}$ $y=101/487$

Explanation:

$16 x + 13 y = 7$ $16x+13y=7$
$- 19 x + 15 y = - 2$ $-19x+15y=-2$

Multiply top equation by $15$ $15$ and second linear equation by $13$ $13$ to make the values of $y$ $y$ the same so they cancel out when subtracted from each other:

$240 x + 195 y = 105$ $240x+195y=105$
$- 247 x + 195 y = - 26$ $-247x+195y=-26$
which gives:
$487 x = 131$ $487x=131$ when subtracted from each other.
$x = \frac{131}{487}$ $x=131/487$

Substitute $x$ $x$ into first original equation:

$16 (\frac{131}{487}) + 13 y = 7$ $16(131/487)+13y=7$
$(\frac{2096}{487}) + 13 y = 7$ $(2096/487)+13y=7$
$13 y = 7 - (\frac{2096}{487})$ $13y=7-(2096/487)$
$13 y = (\frac{1313}{487})$ $13y=(1313/487)$
$y = \frac{(\frac{1313}{487})}{13}$ $y=((1313/487))/13$
$y = \frac{101}{487}$ $y=101/487$

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How do you solve the following system?: $16 x + 13 y = 7, - 19 x + 15 y = - 2$ $16x +13y =7, -19x +15y = -2$

2 Answers

Explanation:

Explanation:

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How do you solve the following system?: $16 x + 13 y = 7, - 19 x + 15 y = - 2$ $16x +13y =7, -19x +15y = -2$