How do you solve the following system: $x + 8 y = 15, 5 x - 7 y = 12$ $x + 8y = 15 , 5x - 7y = 12$ ?

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How do you solve the following system: $x + 8 y = 15, 5 x - 7 y = 12$ $x + 8y = 15 , 5x - 7y = 12$ ?

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Answer 1 · 2018-05-23T12:16:28

See a solution process below:

Explanation:

Step 1) Solve the first equation for $x$ $x$ :

$x + 8 y = 15$ $x + 8y = 15$

$x + 8 y - 8 y = 15 - 8 y$ $x + 8y - color(red)(8y) = 15 - color(red)(8y)$

$x + 0 = 15 - 8 y$ $x + 0 = 15 - 8y$

$x = 15 - 8 y$ $x = 15 - 8y$

Step 2) Substitute $(15 - 8 y)$ $(15 - 8y)$ for $x$ $x$ in the second equation and solve for $y$ $y$ :

$5 x - 7 y = 12$ $5x - 7y = 12$ becomes:

$5 (15 - 8 y) - 7 y = 12$ $5(15 - 8y) - 7y = 12$

$(5 \times 15) - (5 \times 8 y) - 7 y = 12$ $(5 xx 15) - (5 xx 8y) - 7y = 12$

$75 - 40 y - 7 y = 12$ $75 - 40y - 7y = 12$

$75 + (- 40 - 7) y = 12$ $75 + (-40 - 7)y = 12$

$75 + (- 47) y = 12$ $75 + (-47)y = 12$

$75 - 47 y = 12$ $75 - 47y = 12$

$75 - 75 - 47 y = 12 - 75$ $75 - color(red)(75) - 47y = 12 - color(red)(75)$

$0 - 47 y = - 63$ $0 - 47y = -63$

$- 47 y = - 63$ $-47y = -63$

$\frac{- 47 y}{- 47} = - \frac{63}{- 47}$ $(-47y)/color(red)(-47) = -63/color(red)(-47)$

$y = \frac{63}{47}$ $y = 63/47$

Step 3) Substitute $\frac{63}{47}$ $63/47$ for $y$ $y$ in the solution to the first equation at the end of Step 1 and calculate $x$ $x$ :

$x = 15 - 8 y$ $x = 15 - 8y$ becomes:

$x = 15 - (8 \times \frac{63}{47})$ $x = 15 - (8 xx 63/47)$

$x = 15 - \frac{504}{47}$ $x = 15 - 504/47$

$x = (\frac{47}{47} \times 15) - \frac{504}{47}$ $x = (47/47 xx 15) - 504/47$

$x = \frac{705}{47} - \frac{504}{47}$ $x = 705/47 - 504/47$

$x = \frac{201}{47}$ $x = 201/47$

The Solution Is:

$x = \frac{201}{47}$ $x = 201/47$ and $y = \frac{63}{47}$ $y = 63/47$

Or

$(\frac{201}{47}, \frac{63}{47})$ $(201/47, 63/47)$

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How do you solve the following system: $x + 8 y = 15, 5 x - 7 y = 12$ $x + 8y = 15 , 5x - 7y = 12$ ?

1 Answer

Explanation:

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How do you solve the following system: x+8y=15,5x−7y=12x + 8y = 15 , 5x - 7y = 12 ?

1 Answer

Explanation:

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How do you solve the following system: $x + 8 y = 15, 5 x - 7 y = 12$ $x + 8y = 15 , 5x - 7y = 12$ ?