Question

resolva os sistemas lineares pelo metodo ou adicao

a)2x+3y=13 b)2x-5y=11
3x-5y=10 3x+6y=3


c)x+y=3000
x-y=400
​

Answer 1

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$\large\boxed{\begin{array}{l}\tt a)\\\begin{cases}\sf 2x+3y=13\cdot5\\\sf3x-5y=10\cdot3\end{cases}\\+\underline{\begin{cases}\sf10x+\diagdown\!\!\!\!\!\!15y=65\\\sf9x-\diagdown\!\!\!\!\!15y=30\end{cases}}\\\sf 19x=95\\\sf x=\dfrac{95}{19}\\\sf x=5 \\\sf 2x+3y=13\\\sf 2\cdot5+3y=13\\\sf 10+3y=13\\\sf 3y=13-10\\\sf 3y=3\\\sf y=\dfrac{3}{3}\\\sf y=1\\\sf S=\{5,1\}\end{array}}$

$\large\boxed{\begin{array}{l}\tt b)\\\begin{cases}\sf 2x-5y=11\cdot6\\\sf3x+6y=3\cdot5\end{cases}\\+\underline{\begin{cases}\sf12x-\diagdown\!\!\!\!\!\!30\diagdown\!\!\!y=66\\\sf15x+\diagdown\!\!\!\!\!\!30\diagdown\!\!\!y=15\end{cases}}\\\sf 27x=81\\\sf x=\dfrac{81}{27}\\\sf x=3\\\sf 3x+6y=3\div3\\\sf x+2y=1\\\sf 3+2y=1\\\sf 2y=1-3\\\sf 2y=-2\\\sf y=-\dfrac{2}{2}\\\sf y=-1\\\sf S=\{3,-1\}\end{array}}$

$\large\boxed{\begin{array}{l}\tt c)\\+\underline{\begin{cases}\sf x+\diagup\!\!\!y=3000\\\sf x-\diagup\!\!\!y=400\end{cases}}\\\sf 2x=3400\\\sf x=\dfrac{3400}{2}\\\sf x=1700\\\sf x+y=3000\\\sf 1700+y=3000\\\sf y=3000-1700\\\sf y=1300\\\sf S=\{1700,1300\}\end{array}}$