Use the substitution method to solve the system x - 2y = 3, 4x - 8y = 12.
• no solution
• infinite solutions
• (3,0)
• (0,3)
To solve the system of equations using the substitution method, we can solve one equation for one variable and substitute it into the other equation.
From the first equation, we have:
x - 2y = 3
x = 3 + 2y
Now we substitute this expression for x into the second equation:
4x - 8y = 12
4(3 + 2y) - 8y = 12
12 + 8y - 8y = 12
12 = 12
As we can see, the equation simplifies to 12 = 12. This implies that the two equations are equivalent, so they represent the same line. Therefore, the system has infinite solutions.
Answer: infinite solutions