How do solve the following linear system?: $x - 3 y = 8, 3 y = 15 - 6 x$ $x - 3y = 8 , 3y = 15 -6x$ ?

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Answer 1 · 2015-12-05T03:30:43

The solution for the system of equations is :

$x = \frac{23}{7}, y = \frac{- 11}{7}$ $color(blue)(x=23/7, y=(-11)/7$

$x - 3 y = 8$ $x-3y=8$

$x = 8 + 3 y$ $x=color(blue)(8 +3y$ ....................equation $1$ $1$

$3 y = 15 - 6 x$ $3y=15-6x$ ................equation $2$ $2$

Solving by substitution.

Substituting equation $1$ $1$ in $2$ $2$

$3 y = 15 - 6 x$ $3y=15-6x$

$3 y = 15 - 6 \cdot (8 + 3 y)$ $3y=15-6 * (color(blue)(8 +3y))$

$3 y = 15 - 48 - 18 y$ $3y=15- 48 -18y$

$3 y + 18 y = 15 - 48$ $3y+18y=15- 48$

$21 y = - 33$ $21y=- 33$

$y=(-cancel33)/cancel21$

$color(blue)(y=(-11)/7$

Now, we substitute this value of $y$ in equation $1$ to find $x$

$x=8 +3y$

$x=8 +3 * (-11/7)$

$x=8 -33 /7$

$x=56/7 -33 /7$

$color(blue)(x=23/7$

How do solve the following linear system?: x - 3y = 8 , 3y = 15 -6x x−3y=8,3y=15−6x x - 3y = 8 , 3y = 15 -6x ?