Question

Como resolvo----------- 3x-2y=10
5x+2y=22
= ?????

Answer 1

3x - 2y = 10
5x + 2y = 22

8x = 32
x = 4

5x + 2y = 22
5 . 4 + 2y = 22
20 + 2y = 22
2y = 22 - 20
2y = 2
y = 1

S = { 4 ; 1 }

Answer 2

Por  Comparação:

$\left \{ {{3x-2y=10} \atop {5x+2y=22}} \right. \\\\\\3x-2y=10\to 3x=2y+10\to x= \frac{2y+10}{3} \\\\5x+2y=22\to 5x=-2y+22\to x= \frac{-2y+22}{5} \\\\\\\\ \frac{2y+10}{3} = \frac{-2y+22}{5}\to 5(2y+10)=3(-2y+22)\to \\\\ 10y+50=-6y+66\to 10y+6y=66-50\to 16y=16\to y= \frac{16}{16}\to \\\\ y=1$



$x=\frac{2y+10}{3} \to x=\frac{2*1+10}{3} \to x=\frac{2+10}{3} \to x=\frac{12}{3} \to x=4 \\\\x= \frac{-2y+22}{5}\to x= \frac{-2*1+22}{5}\to x= \frac{-2+22}{5}\to x= \frac{20}{5}\to x=4\\\\\\ S= \left \{ 4;1 \left \}$