Use the substitution method to solve the system 2x+3y=4 , −4x−6y=−8 .(1 point)
Responses
infinite solutions
infinite solutions
(2−1)
left parenthesis 2 comma negative 1 right parenthesis
no solution
no solution
(−1,2)
To solve the system of equations using the substitution method, we solve one equation for one variable and substitute it into the other equation.
Let's solve the first equation for x:
2x + 3y = 4
2x = 4 - 3y
x = (4 - 3y)/2
Now substitute 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
The equation -8 = -8 is true, which means the system has infinite solutions. Therefore, the correct response is "infinite solutions."