Question

Solve the system using substitution method 3x+y=6 2x-4y=10

Answer 1

$\left\{\begin{array}{ccc}3x+y=6&|-3x\\2x-4y=10\end{array}\right\\\\\left\{\begin{array}{ccc}y=6-3x\\2x-4y=10\end{array}\right\\\\substitute\ y=6-3x\ to\ the\ second\ equation\\\\2x-4(6-3x)=10\\\\2x-4\cdot6-4\cdot(-3x)=10\\\\2x-24+12x=10\\\\14x-24=10\ \ \ |+24\\\\14x=34\ \ \ \ |:14\\\\x=\dfrac{34}{14}\to x=\dfrac{17}{7}\\\\substitute\ the\ value\ of\ x\ to\ first\ equation\\\\y=6-3\cdot\dfrac{17}{7}=6-\dfrac{51}{7}=\dfrac{42}{7}-\dfrac{51}{7}=-\dfrac{9}{7}$

$\boxed{\left\{\begin{array}{ccc}x=\dfrac{17}{7}\\\\y=-\dfrac{9}{7}\end{array}\right}$

Answer 2

$\begin{cases}&3x + y = 6 \\&2x - 4y = 10\end{cases}$

Multiply 4 to the first equation:
$\begin{cases}&12x + 4y = 24 \\&2x - 4y = 10\end{cases}$

ADD Equation 1 to Equation 2 and find x:
$\begin{aligned}&14x =34 \\&x= 34/14 \\& x = 17/7\end{aligned}$

Substitute x = 17/7 and find y:
$\begin{aligned}&3x + y = 6 \\&3 (17/7) + y = 6 \\& 51/7 + y = 6 \\&y = -9/7\end{aligned}$

Answer: x = 17/7, y  = -9/7