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

Question

Responses

infinite solutions
infinite solutions

(2−1)
left parenthesis 2 comma negative 1 right parenthesis

no solution
no solution

(−1,2)

Answer 1

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."