For questions 4–5, how many solutions does the system have?
–4y + 4 = x
2x + 8y = 8
(1 point)
Responses
one solution
one solution
two solutions
two solutions
infinitely many solutions
infinitely many solutions
no solution
no solution
The system of equations is:
–4y + 4 = x
2x + 8y = 8
To determine the number of solutions, we can compare the slopes of the two equations.
The first equation can be rewritten as x = 4y + 4, which has a slope of 4.
The second equation can be rewritten as x/2 + 4y = 4, which can be simplified to x + 8y = 8. This equation also has a slope of 4.
Since the slopes are equal, the system has infinitely many solutions.
The correct answer is: infinitely many solutions