Question

Use the substitution method to solve the system 2x+3y=4 , −4x−6y=−8 .(1 point)Responses(2−1)left parenthesis 2 comma negative 1 right parenthesis(−1,2)left parenthesis negative 1 comma 2 right parenthesisno solutionno solutioninfinite solutions

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve the system of equations using the substitution method, we will solve one equation for one variable and substitute that expression into the other equation.

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

Now we 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 true for any value of y, meaning that there are infinite solutions.

The solution for the system of equations is "infinite solutions."