Step-by-step explanation:
2x + 3z = 17
3x + 4z = 24
FYI - this is not a situation, where I would choose the elimination method ("equation arithmetic") to solve the system of equations, because none of the terms is the same or numerically "compatible", so that I need to multiply only one equation with an integer before adding or subtracting the equations.
basically it is very similar to fraction arithmetic. but instead of bringing 2 fractions to the same denominator, we need to bring one of the terms to the same factor.
so, let's bring both equations to 6x terms (6 being the smallest common multiple of 2 and 3) and then subtract the second from the first equation :
6x + 9z = 51
- 6x + 8z = 48
----------------------
0 + z = 3
=> e.g. via the first original equation :
2x + 3×3 = 17
2x + 9 = 17
2x = 8
x = 4
