For the following system of equations, what is the x-value of the solution $- x + 2 y = 6, 6 y = x + 18$ $-x+2y=6, 6y=x+18$ ?

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Answer 1 · 2017-01-10T22:08:01

$x = 0$ $x = 0$

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

$- x + 2 y = 6$ $-x + 2y = 6$

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

$0 + 2 y = 6 - x$ $0 + 2y = 6 - x$

$2 y = 6 - x$ $2y = 6 - x$

$\frac{2 y}{2} = \frac{6 - x}{2}$ $(2y)/color(red)(2) = (6 - x)/color(red)(2)$

$(color(red)(cancel(color(black)(2)))y)/cancel(color(red)(2)) = 6/2 - x/2$

$y = 3 - x/2$

Step 2) Substitute $3 - x/2$ for $y$ in the second equation and solve for $x$ :

$6(3 - x/2) = x + 18$

$18 - (6x)/2 = x + 18$

$18 - 3x = x + 18$

$18 - 3x + color(red)(3x) - color(blue)(18) = x + 18 + color(red)(3x) - color(blue)(18)$

$18 - color(blue)(18) - 3x + color(red)(3x) = x + color(red)(3x) + 18 - color(blue)(18)$

$0 - 0 = 4x + 0$

$0 = 4x$

$0/color(red)(4) = (4x)/color(red)(4)$

$0 = (color(red)(cancel(color(black)(4)))x)/cancel(color(red)(4))$

$0 = x$

$x = 0$

For the following system of equations, what is the x-value of the solution -x+2y=6, 6y=x+18−x+2y=6,6y=x+18-x+2y=6, 6y=x+18?