To solve this system of equations using substitution, we will first solve the second equation for y in terms of x.
Equation 2: y - 2x + 4 = 0
Now, isolate y:
y = 2x - 4
Next, substitute this expression for y in the first equation:
6x = 3(2x - 4) + 2
Now, distribute the 3 on the right side of the equation:
6x = 6x - 12 + 2
Next, subtract 6x from both sides:
0 = -12 + 2
Now, add 12 to both sides:
12 = 2
This statement is false, which means there is no solution to this system of equations. The two lines represented by these equations do not intersect, so they are parallel.
