How do solve the following linear system?: $3x - y = -6, y = 5x - 7$ ?

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Answer 1 · 2017-08-27T17:56:20

See a solution process below: $(13/2, 51/2)$

Step 1) Because the second equation is already solved for $y$ we can substitute $(5x - 7)$ for $y$ in the first equation and solve for $x$ :

$3x - y = -6$ becomes:

$3x - (5x - 7) = -6$

$3x - 5x + 7 = -6$

$(3 - 5)x + 7 = -6$

$-2x + 7 = -6$

$-2x + 7 - color(red)(7) = -6 - color(red)(7)$

$-2x + 0 = -13$

$-2x = -13$

$(-2x)/color(red)(-2) = (-13)/color(red)(-2)$

$(color(red)(cancel(color(black)(-2)))x)/cancel(color(red)(-2)) = 13/2$

$x = 13/2$

Step 2) Substitute $13/2$ for $x$ in the second equation and calculate $y$ :

$y = 5x - 7$ becomes:

$y = (5 * 13/2) - 7$

$y = 65/2 - (2/2 xx 7)$

$y = 65/2 - 14/2$

$y = 51/2$

The Solution Is: $x = 13/2$ and $y = 51/2$ or $(13/2, 51/2)$

How do solve the following linear system?: 3x - y = -6, y = 5x - 7 3x - y = -6, y = 5x - 7?