Answer:
D. [tex]x=-1, y=2\frac{2}{3}[/tex]
Step-by-step explanation:
Solving for x:
2x+3y=6
Subtract 3y from both sides
2x= -3y+6
Subtract 6 from both sides
2x-6= -3y
-4x+3y=12
Subtract 3y from both sides
-4x= -3y+12
Subtract 12 from both sides
-4x-12= -3y
Combine equations:
-4x-12=2x-6
Add 4x to both sides
-12=6x-6
Add 6 to both sides
-6=6x
6x= -6
Divide both sides by 6
x= -1
Solving for y:
2x+3y=6
Subtract 3y from both sides
2x= -3y+6
-3y+6=2x
Multiply both sides by -1
3y-6= -2x
Multiply both sides by 2
6y-12= -4x
-4x+3y=12
Subtract 3y from both sides
-4x= -3y+12
-3y+12= -4x
Combine equations:
6y-12= -3y+12
Add 3y to both sides
9y-12=12
Add 12 to both sides
9y=24
Divide both sides by 9
y= [tex]2\frac{2}{3}[/tex]
