Question

Use the substitution method to solve the system 2x+3y=4 , −4x−6y=−8

(2, −1)


(−1, 2)

no solution

infinite solutions

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.

From the first equation, we can solve for x:

2x + 3y = 4 (equation 1)
2x = 4 - 3y
x = 2 - (3/2)y

Now, substitute x = 2 - (3/2)y into the second equation:

-4x - 6y = -8 (equation 2)
-4(2 - (3/2)y) - 6y = -8
-8 + 6y - 6y = -8
-8 = -8

The equation -8 = -8 is true, which means that both equations are for the same line. The system has infinitely many solutions because all the points on the line satisfy both equations.

Therefore, the correct answer is infinite solutions.