Use the substitution method to solve the system 2x+3y=4 , −4x−6y=−8 .(1 point)Responses(−1,2)left parenthesis negative 1 comma 2 right parenthesis(2−1)left parenthesis 2 comma negative 1 right parenthesisinfinite solutionsinfinite solutionsno solution

Answer 1

To solve the system using the substitution method, we can solve one equation for one variable and substitute it into the other equation.

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

Rearranging the equation, we have:
2x = 4 - 3y
x = (4 - 3y)/2

Substituting this expression for x into the second equation, we have:
-4((4 - 3y)/2) - 6y = -8

Multiplying through by 2 to eliminate the denominator, we have:
-8 + 6y - 6y = -16
-8 = -16

This equation is not true. Therefore, there is no solution to the system of equations.