Use the substitution method to solve the system 2x+3y=4, −4x−6y=−8.
To solve the system using the substitution method, we will solve one equation for one variable and substitute it into the other equation.
Let's start by isolating one variable in the first equation:
Rearrange the first equation 2x + 3y = 4 to solve for x:
2x = 4 - 3y
x = (4 - 3y) / 2
Now, substitute this value of x into the second equation:
-4x - 6y = -8
-4((4 - 3y)/2) - 6y = -8
-2(4 - 3y) - 6y = -8
-8 + 6y - 6y = -8
-8 = -8
Since -8 = -8 is true, it means that the system of equations is dependent. This means that the two equations represent the same line, and there are infinite solutions. The system is consistent and dependent.