Hi, I don’t understand the technique here - what’s meant by subtract 1 from each side in the solution?
Solution expanded:
Subtract equation 1 from equation 2.
( 2x + 3y + 4z ) - ( x + 2y + 3z ) = 11-5
We get,
x + y + z = 6
Subtract equation 2 from equation 3.
( 3x + 4y + 5z ) - ( 2x + 3y + 4z ) = 85-11
We get,
x + y + z = 74
Notice that this implies that 6=74, which is not possible. Hence the correct answer is option C.
1 Like
Thanks Joan! That’s very helpful. Why did you choose to subtract equation 2 from 3 and not that the other way round? is it because equation 3 subtracted from equation 2 would result in negative coefficients with which you would have to multiply -1 across the equation to land up at the same equation and you could foresee that?
and generally, how do you identify if you need to carry out this operation at all? do you just keep adding and subtracting equations within the system at random to figure out if it has 0 solutions?
Yes, I noticed that coefficients in equation 3 is larger than the coefficients in equation 2. So if we subtract equation 2 from 3, we will have positive coefficients.
The objective in general is to see if we could eliminate entire terms by adding or subtraction equations. If that is not possible like in this instance we can deduct that system of equations is not solvable.
I get it now. Thank you!
1 Like