use the substitution method to solve the system 2x+3y=4,-4x-6y=-8.
infinite solutions
no solutions
(-1,2)
(2,-1)
To use the substitution method, we solve one equation for one variable and substitute it into the other equation.
From the first equation, we solve for x in terms of y:
2x + 3y = 4
2x = 4 - 3y
x = (4 - 3y)/2
Now we substitute this expression for x into the second equation:
-4x - 6y = -8
-4((4 - 3y)/2) - 6y = -8
Simplifying this equation:
-2(4 - 3y) - 6y = -8
-8 + 6y - 6y = -8
-8 = -8
This equation is true, which means the system of equations has infinitely many solutions. Hence, the correct answer is:
infinite solutions