Answer:
A=4
A=12/3
Step-by-step explanation:
To determine the value of "a" that would make the given system of equations have an infinite number of solutions, we need to check if the two equations are dependent or consistent.
Write the system of equations in standard form:
2x - 3y = 6 ...(1)
4x - 6y = 3a ...(2)
Multiply equation (1) by 2 to make the coefficients of "x" the same in both equations:
4x - 6y = 12 ...(3)
Compare equations (2) and (3):
4x - 6y = 3a ...(2)
4x - 6y = 12 ...(3)
Analyze the comparison:
If the two equations have the same left-hand side and different right-hand sides, the system has no solution.
If the two equations have the same left-hand side and the same right-hand side, the system has infinitely many solutions.
Set the right-hand sides of equations (2) and (3) equal to each other:
3a = 12
Solve for "a":
Divide both sides of the equation by 3:
a = 12/3
a = 4
Therefore, for the value of "a" equal to 4, the given system of equations would have an infinite number of solutions.