Determine the number of solutions of this system of linear equations:
x+2y=−4
4x+8y=−16
This question requires you to show your work.
(1 point)
Responses
One Solution
One Solution
No Solutions
No Solutions
Infinitely Many Solutions
- Start by multiplying the first equation by -2 to eliminate x: -2(x+2y) = -2(-4), which simplifies to -2x - 4y = 8.
- Now compare this new equation with the second given equation: -2x - 4y = 8, 4x + 8y = -16.
- Since the two equations are the same, the system is dependent or consistent with infinitely many solutions.