Use the substitution method to solve the system 2x + 3y = 4, -4x -6y= -8.
• infinite solutions
• 2-1)
• (-1,2)
• no solution
To solve the system using the substitution method, we'll solve one equation for one variable and then substitute that expression into the other equation.
Let's solve the first equation for x:
2x + 3y = 4
2x = 4 - 3y
x = (4 - 3y)/2
Now we'll substitute this expression for x into the second equation:
-4x - 6y = -8
-4((4 - 3y)/2) - 6y = -8
-(2(4 - 3y)) - 6y = -8
-(8 - 6y) - 6y = -8
-8 + 6y - 6y = -8
-8 = -8
The equation simplifies to -8 = -8, which is always true. This means that the system has an infinite number of solutions. So, the correct answer is: infinite solutions.