What values of x and y satisfy x + 2y = 6 and 2x + 3y = 4 simultaneously?

First take x + 2y = 6 and isolate x:
x = 6 - 2y
Then substitute that for x in 2x + 3y = 4:
2(6 - 2y) + 3y = 4
12 - 4y + 3y = 4
12 - y = 4
-y = -8
y = 8
Substitute y = 8 into x + 2y = 6 and 2x + 3y = 4:
x + 2(8) = 6 --> x + 16 = 6 --> x = -10
2x + 3(8) = 4 --> 2x + 24 = 4 --> 2x = -20 --> x = -10
y = 8 and x = -10

X + 2y = 6
2x + 3y = 4


x = 6 - 2y 

2(6-2y) + 3y = 4
12 - 4y + 3y = 4
12 - y = 4
-y = - 8 
y = 8

x = 6 - 2 * 8 = 6 - 16 = -10