Question

Use the substitution method to solve the system 2x + 3y=4-4x -6y=-8.
(2-1)
No solution
Infinite solution
(-1,2)

Answer 1

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

Let's solve the first equation for x:
2x + 3y = 4
Solving for x, we get:
2x = 4 - 3y
x = (4 - 3y)/2

Now, substitute this value of 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 always true, meaning that the system has an infinite number of solutions. So, the answer is "Infinite solution."