Determine and select the value of c that makes 3x - 5y = 9 and -0.6x + y = c be a system of equations with infinitely many solutions.

a. 0.6
b. -9
c. 9
d. equation
e. -1.8

Question

Determine and select the value of c that makes 3x - 5y = 9 and -0.6x + y = c be a system of equations with infinitely many solutions.

a. 0.6
b. -9
c. 9
d. equation
e. -1.8

anonymous · Answer

The only way a system of 2 variable linear equations can have infinitely many solutions is if the x and y coefficients are related and the the constants the right side of the equal sign are related in the same way.  Multiply the second equation by -5 -> 3x - 5y = -5c.  -5c must equal 9 for there to be infinitely many solutions, so -5c = 9 -> c = -9/5