Which value, when placed in the box, would result in a system of equations with infinitely many solutions? y = -2x + 4 6x + 3y =
2 answers:
Answer:
Option (4)
Step-by-step explanation:
The given system of equations is,
y = -2x + 4 ------ (1)
6x + 3y = a --------(2)
We have to find the value of a for which the system of equations will have infinitely many solutions.
Option (1). If a = -12
6x + 3y = -12
2x + y = -4
y = -2x - 4
Both the equations have same slope, therefore, they are parallel and will have no solutions.
Option (2). If a = -4
6x + 3y = -4
3y = -6x - 4
Then equation (1) and (2) will intersect each other at least at one point Or there is exactly one solution of the system of the equations.
Option (3). If a = 4
6x + 3y = 4
3y = -6x + 4
y = -2x +
Then equation (1) and (2) will intersect each other at least at one point Or there is exactly one solution of the system of the equations.
Option (4). If a = 12
6x + 3y = 12
3y = -6x + 12
y = -2x + 4
Therefore, both the equations (1) and (2) are same for a = 12 and they will have infinitely many solutions.
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