Question

Alvin’s first step in solving the given system of equations is to multiply the first equation by 2 and the second equation by –3. Which linear combination of Alvin’s system of equations reveals the number of solutions to the system?
9x + 4y = 36

6x + 2.5y = 24

Answer 1

The answer 

9x + 4y = 36           (times 2) implies      18x + 8y = 72     (a)

6x + 2.5y = 24        (times -3) imiplies    18x + 7.5y =72   (b)

so (a) - (b)            8-7.5)y=0, and y=0

when y=o  18x + 8. 0= 72 implies x =4

so the solution is (4,0)

Answer 2

After multiplying by the stated coefficients and adding, the equation obtained is:
8y - 7.5y = 0
y = 0
x = 4

Because the two equations formed were independent, they had one solution.