Question

3x + 6y = 12
2x + 6y = -10

Answer 1

3x + 6y=12
2x +6y=-10 •(-1)

3x + 6y=12 (1)
-2x - 6y=10 (2)
=> x=22

X em (1):
3 • 22 + 6y=12
66 + 6y=12
6y=-66 + 12
6y=-54
Y=-9

Answer 2

Por comparação:

$\left \{ {{3x+6y=12} \atop {2x+6y=-10}} \right. \\\\\\ 3x+6y=12\to 3x=-6y+12\to x= \frac{-6y+12}{3} \\\\ \\ 2x+6y=-10\to 2x=-6y-10\to x= \frac{-6y-10}{2} \\\\\\\\ \frac{-6y+12}{3} =\frac{-6y-10}{2} \to 2*(-6y+12)=3*(-6y-10)\to \\\\-12y+24=-18y-30\to -12+18y=-30-24\to \\\\ 6y=-54\to y= \frac{-54}{6} \to y=-9$



$\\\\\\ x= \frac{-6y+12}{3}\to x= \frac{-6*(-9)+12}{3}\to x= \frac{54+12}{3}\to x= \frac{66}{3}\to x=22 \\\\\\x= \frac{-6y-10}{2}\to x= \frac{-6*(-9)-10}{2} \to x= \frac{54-10}{2} \to x= \frac{44}{2} \to x=22\\\\\\\\ S= \left \{22; -9\left \}$