A student took a system of equations, multiplied the first equation by 2 and the second equation by 3, then added the results together. Based on this, she concluded that there were no solutions. Which system of equations could she have started with?
a) 2x - 4y = 6
-3x + 6y = 9
b) 3x + 6y = 9
-2x - 4y = 4
c)3x + y = 12
-3x + 6y = 6
d)-2x + 4y = 4
-3x + 6y = 6
1 answer
The correct answer is d) -2x + 4y = 4 and -3x + 6y = 6. This is because when the first equation is multiplied by 2, it becomes -4x + 8y = 8, and when the second equation is multiplied by 3, it becomes -9x + 18y = 18. Adding these two equations together results in -13x + 26y = 26. This equation has no solutions because there are no common factors between -13, 26, and 26.
1 answer