How do you solve the system of equations $8x+4y=13$ and $-2x=y+4$ ?

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Answer 1 · 2017-05-03T13:46:18

See the entire solution process below:

First, sole the second equation for $y$ :

$-2x = y + 4$

$-2x - color(red)(4) = y + 4 - color(red)(4)$

$-2x - 4 = y + 0$

$-2x - 4 = y$

$y = -2x - 4$

Step 2) Substitute $-2x - 4$ for $y$ in the first equation and solve for $x$ :

$8x + 4y = 13$ becomes:

$8x + 4(-2x - 4) = 13$

$8x + (4 * -2x) - (4 * 4) = 13$

$8x -8x - 16 = 13$

$0 - 16 = 13$

$-16 != 13$

Therefore, there are no solutions to this problem. Or, the solution is the empty or null set: ${O/}$ .

This means the two lines defined by these equations are parallel and are not the same line.

How do you solve the system of equations 8x+4y=138x+4y=13 and -2x=y+4-2x=y+4?