Answer:
2
Step-by-step explanation:
You want to know the multiplier for the second equation if you want to eliminate the x-variable by adding the multiplied equation to 3 times the first equation.
In general, the procedure for eliminating a variable will be to multiply each equation by the coefficient of that variable in the other equation, then subtracting one result from the other.
If you want to add the multiplied equations, then one of the multipliers must be the opposite of the coefficient it is derived from.
Here, the x-coefficients are ...
first equation: 2
second equation: -3
You have chosen to multiply the first equation by 3, the opposite of -3, so the second equation must be multiplied by 2 (the unchanged coefficient of x in the first equation).
You want the equations to add such that the x-coefficient is zero. For some multiplier k of the second equation. the resulting x-coefficient will be ...
3(2x) +k(-3x) = 0x
(6 -3k)x = 0x
6 -3k = 0 . . . . . . . . equate coefficients of x
6 = 3k . . . . . . . . add 3k
k = 6/3 = 2 . . . . . . the multiplier of the second equation
(Note that this is the coefficient of x in the first equation.)
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