Subject: college algebra
Name: katrina
Who are you: Student

solve the system of equations using either the substitution or the elimination
method.

2x-3y= -12 and -4x+6y=15

Hi Katrina,

I think I see your difficulty with this problem. Whichever technique you try you arrive at an equation that makes no sense. The reason is that there are no numbers x and y that satisfy the equations.

The first equation says that

2x - 3y = 12

Now look at the left side of the second equation. There is a common factor of -2, thus the left side of the second equation is

-4x + 6y = -2(2x - 3y)

If x and y satisfy the first equation then 2x - 3y = 12 but then the left side of the second equation is

-2(2x - 3y) = -2(12) = -24

But if x and y satisfy the second equation this value must be 15. Hence if x and y satisfy the first equation they can't satisfy the second and thus the system of equations has no solution.

Penny