We have the next system of equations
2x+3y=10
4x+6y=12
We will multiply by -2 the first equation
-2(2x+3y=10)
-4x-6y=-20
Then we sum the equation above with the second equation
4x+6y=12
+ -4x-6y=-20
___________
0 + 0=-8
as we can see we have 0=-8, which is false and it is incongruent, therefore the system has no solution.
We need to calculate two points for each equation
For 2x+3y=10
if x=0
2(0)+3y=10
3y=10
y= 10/3
point (0,10/3)
if y=0
2x+3(0)=10
2x=10
x=10/2
x=5
Point (5,0)
for 4x+6y=12
if x=0
4(0)+6y=12
6y=12
y=12/6
y=2
Point (0,2)
if y=0
4x+6(0)=12
4x=12
x=12/4
x=3
Point (3,0)
Then we graph the point and we connect them
As we can see we have parallel lines therefore the system of equations has no solution.
ANSWER
no solution