Question

Simultaneous equation
Find x and y
2x+y=5
X+3y=5

Answer 1

`Elimination\ method:\\ \left\{\begin{array}{ccc}2x+y=5\\x+3y=5&|multiply\ both\ sides\ by\ (-2)\end{array}\right\\+\left\{\begin{array}{ccc}2x+y=5\\-2x-6y=-10\end{array}\right\ \ \ |add\ sides\ of\ the\ equations\\------------\\.\ \ \ \ -5y=-5\ \ \ \ \ |divide\ both\ sides\ by\ (-5)\\.\ \ \ \ \ \ \ \boxed{y=1}\\\\substitute\ the\ value\ of\ y\ into\ one\ of\ the\ equations\ (\#2)\\\\x+3*1=5\\x+3=5\ \ \ \ \ \ |subtract\ 3\ from\ both\ sides\\\boxed{x=2}\\\center\boxed{Answer:x=2\ and\ y=1\to(2;\ 1)}`

Answer 2

`x+3y=5 \ =>\boxed{x=5-3y} \\\\ 2x+y=5 \\\\ 2(5-3y)+y=5 \\\\10-6y+y=5 \\\\ -5y=5-10 \\\\ -5y=-5 \ |:(-5) \\\\ \boxed{y=1} \\\\ x=5-3*1 \\\\ x=5-3 \\\\ \boxed{x=2}`