Use the substitution method to solve the system 2x+3y=4 , −4x−6y=−8 .(1 point)

Answer 1

First, solve one of the equations for one of the variables in terms of the other variable.

From the first equation, we can solve for x in terms of y:
2x + 3y = 4
2x = 4 - 3y
x = (4 - 3y)/2

Now, substitute this expression for x in the second equation:
-4x - 6y = -8
-4*(4 - 3y)/2 - 6y = -8
-2(4 - 3y) - 6y = -8
-8 + 6y - 6y = -8
-8 = -8

This equation is always true, which means that the system of equations is dependent or has infinitely many solutions. The two equations represent the same line.