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
No Solutions No Solutions
One Solution One Solution
Infinitely Many Solutions Infinitely Many Solutions
Show Your Work. Do Not Use Matrix to solve.
To determine the number of solutions of the system of linear equations, we can rewrite the second equation as 4(x+2y) = -16. This simplifies to 4(-4) = -16, which is true. This means that the second equation is actually a multiple of the first equation.
Therefore, the two equations represent the same line, and there are infinitely many solutions to this system of linear equations.