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

User RWGodfrey
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2 Answers

2 votes

\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
User Boindiil
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8.5k points
4 votes

\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=(34)/(14)\to x=(17)/(7)\\\\substitute\ the\ value\ of\ x\ to\ first\ equation\\\\y=6-3\cdot(17)/(7)=6-(51)/(7)=(42)/(7)-(51)/(7)=-(9)/(7)


\boxed{\left\{\begin{array}{ccc}x=(17)/(7)\\\\y=-(9)/(7)\end{array}\right}
User Falon
by
7.9k points

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