Answer:
multiply the second equation by 9
Step-by-step explanation:
You want to know how to create opposite terms for the x-variable in the system of equations ...
The coefficients of x in the two equations are 3 and -1/3. The ratio of these coefficients is ...
3/(-1/3) = 3 × (-3/1) = -9
Multiplying the second equation by 9 will make the x-terms have opposite coefficients.
9(-1/3x +4y) = 9(6)
-3x +36y = 54 . . . . . . . the x-coefficient is -3
The x-coefficient of -3 is now opposite the x-coefficient of 3 in the first equation.
Opposite x-coefficients can be created by multiplying the second equation by 9.
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Additional comment
When terms with the same variable have coefficients that have an integer ratio, the coefficients can be made opposites by multiplying or dividing one of the equations by the opposite of that ratio. Here the ratio is -9, so multiplying the equation with the smaller coefficient by +9 makes the coefficients opposites.
We could also divide the first equation by +9 to make the x-coefficients opposites. That would give 1/3x -2/3y = -8/9. The x-coefficient of 1/3 is now the opposite of the x-coefficient of -1/3 in the second equation.
Generally we like to work with integers, so that approach might not be a first choice.
The solution to this system is (x, y) = (2/5, 23/15).
