X +2y=-4. 4x + 8y= -16 determine the number of solutions of the system of linear equations a infinitely many solutions B one solution or c no solutions
This system of linear equations can be solved using substitution or elimination method.
When we simplify the first equation, we get:
x + 2y = -4 => x = -4 - 2y.
Substitute this value of x into the second equation:
4(-4 - 2y) + 8y = -16
-16 - 8y + 8y = -16
-16 = -16
The equation simplifies to -16 = -16, which represents a consistent and dependent system. This means that the two equations are equivalent and would lie on top of each other when graphed. As a result, this system of linear equations has infinitely many solutions.
Therefore, the correct answer is A. infinitely many solutions.