How do you solve the following system: $-6x + y = -8, -3x + y = -4$ ?

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Answer 1 · 2017-01-31T23:27:58

See the entire solution process below:

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

$-6x + y = -8$

$-6x + color(red)(6x) + y = color(red)(6x) - 8$

$0 + y = 6x - 8$

$y = 6x - 8$

Step 2) Substitute $6x - 8$ for $y$ in the second equation and solve for $x$ :

$-3x + (6x - 8) = -4$

$-3x + 6x - 8 = -4$

$(-3 + 6)x - 8 = -4$

$3x - 8 = -4$

$3x - 8 + color(red)(8) = -4 + color(red)(8)$

$3x - 0 = 4$

$3x = 4$

$(3x)/color(red)(3) = 4/color(red)(3)$

$(color(red)(cancel(color(black)(3)))x)/cancel(color(red)(3)) = 4/3$

$x = 4/3$

Step 3) Substitute $4/3$ for $x$ in the solution to the first equation at the end of Step 1 and calculate $y$ :

$y = (6 xx 4/3) - 8$

$y = 24/3 - 8$

$y = 8 - 8$

$y = 0$

The solution is: $x = 4/3$ and $y = 0$

How do you solve the following system: -6x + y = -8, -3x + y = -4 -6x + y = -8, -3x + y = -4 ?