Respuesta :
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
[tex]y=-2x-\frac{4}{3}[/tex]
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 + [tex]\frac{4}{3}[/tex]
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.
This question is based on system of linear equation .Thus, for a=12 will have infinitely many solution.
Given:
y = -2x + 4 ------ (a)
6x + 3y = a ------(b)
We need to determined the value of a for which the system gives infinitely many solution.
Now check all the options as given below:
Option(1) a = -12 and put it in (b) we get,
6x + 3y = -12
2x + y = -4
y = -2x - 4
Both the equations have same slope, therefore, they are parallel to each other and have no solutions.
Option(2) a= -4 and put it in (b) we get,
6x + 3y = -4
3y = -6x - 4
[tex]y=-2x-\dfrac{4}{3}[/tex]
Therefore, the equation has unique solution. Thus, both lines intersect each other at one point and there is unique value of x and y.
Option(3) a= 4
6x + 3y = 4
3y = -6x + 4
[tex]y=-2x+\dfrac{4}{3}[/tex]
Therefore, the equation has unique solution. Thus, both lines intersect each other at one point and there is unique value of x and y.
Option(4) a= 12
6x + 3y = 12
3y = -6x + 12
y = -2x + 4
Both the equation are same for a= 12.
Thus, for a=12 will have infinitely many solution.
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https://brainly.com/question/13712241
