Use the substitution method to solve the system 2x+3y=4 , −4x−6y=−8 .(1 point) Responses no solution no solution (2−1) left parenthesis 2 comma negative 1 right parenthesis infinite solutions infinite solutions (−1,2)
To solve the system using the substitution method, we will first solve one equation for one variable and substitute that expression into the other equation.
First, we'll solve the first equation for x:
2x + 3y = 4
2x = 4 - 3y
x = (4 - 3y)/2
Now, substitute this expression for x into the second equation:
-4((4 - 3y)/2) - 6y = -8
-2(4 - 3y) - 6y = -8
-8 + 6y - 6y = -8
-8 = -8
The equation -8 = -8 is true, which means that the two equations are equivalent. This indicates that the system has infinitely many solutions. Therefore, the correct answer is "infinite solutions."