How do solve the following linear system?: $5 x - 5 y = 10, - 4 x - 14 y = 28$ $5x-5y=10 , -4x-14y=28$ ?

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How do solve the following linear system?: $5 x - 5 y = 10, - 4 x - 14 y = 28$ $5x-5y=10 , -4x-14y=28$ ?

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Answer 1 · 2017-02-09T14:18:43

See the entire solution process below:

Explanation:

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

$5 x - 5 y = 10$ $5x - 5y = 10$

$5 x - 5 y + 5 y = 10 + 5 y$ $5x - 5y + color(red)(5y) = 10 + color(red)(5y)$

$5 x - 0 = 10 + 5 y$ $5x - 0 = 10 + 5y$

$5 x = 10 + 5 y$ $5x = 10 + 5y$

$\frac{5 x}{5} = \frac{10 + 5 y}{5}$ $(5x)/color(red)(5) = (10 + 5y)/color(red)(5)$

$(color(red)(cancel(color(black)(5)))x)/cancel(color(red)(5)) = 10/color(red)(5) + (5y)/color(red)(5)$

$x = 2 + y$

Step 2) Substitute $2 + y$ for $x$ in the second equation and solve for $y$ :

$-4x - 14y = 28$ becomes:

$-4(2 + y) - 14y = 28$

$-8 - 4y - 14y = 28$

$color(red)(8) - 8 - (4 + 14)y = color(red)(8) + 28$

$0 - 18y= 36$

$-18y = 36$

$(-18y)/color(red)(-18) = 36/color(red)(-18)$

$(color(red)(cancel(color(black)(-18)))y)/cancel(color(red)(-18)) = -2$

$y = -2$

Step 3) Substitute $-2$ for $y$ in the solution to the first equation at the end of Step 1 and calculate $x$ :

$x = 2 + y$ becomes:

$x = 2 + (-2)$

$x = 0$

The solution is: $x = 0$ and $y = -2$

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How do solve the following linear system?: $5 x - 5 y = 10, - 4 x - 14 y = 28$ $5x-5y=10 , -4x-14y=28$ ?

1 Answer

Explanation:

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Impact of this question

Science

Math

Humanities

... and beyond

How do solve the following linear system?: 5x-5y=10 , -4x-14y=28 5x−5y=10,−4x−14y=28 5x-5y=10 , -4x-14y=28 ?

1 Answer

Explanation:

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Impact of this question

How do solve the following linear system?: $5 x - 5 y = 10, - 4 x - 14 y = 28$ $5x-5y=10 , -4x-14y=28$ ?