Question

How many solutions will this system of equations have? x - 2y = 24 3x - 6y = 72

Answer 1

Solve your system of equations.

−2y=24;3x−6y=72

Solve −2y=24 for y:

−2y/−2 = 24/−2(Divide both sides by -2)

y=−12

Substitute (−12) for y in 3x−6y=72:

3x−6y=72

3x+(−6)(−12)=72

3x+72=72(Simplify both sides of the equation)

3x+72+−72=72+−72(Add -72 to both sides)

3x=0

3x/3 = 0/3(Divide both sides by 3)

x=0

Answer B)

Answer 2

$x-2y=24 \ \ \ \ \ \ \ \ \ \ \ \ \ | \times (-3) \\ 3x-6y=72 \\ \\ -3x+6y=-72 \\ \underline{3x-6y=72 \ \ \ \ \ \ \ } \\ 3x-3x+6y-6y=72-72 \\ 0=0 \\ always \ true \\ \\ \hbox{infinitely many solutions}$

The answer is B.