Question

to eliminate the x terms and solve for y in the fewest steps, by which constants should the equations be multiplied by before adding the equations together?
first equation: 6x - 5y = 17
second equation: 7x + 3y = 11
the first equation should be multiplied by 3 and the second equation by -5
the first equation should be multiplied by 3 and the second equation by 5
the first equation should be multiplied by 7 and the second equation by -6
the first equation should be multiplied by 7 and the second equation by 6

Explanation:

Step1: Identify x coefficients

First equation x-coeff: $6$, second: $7$

Step2: Find LCM of coefficients

LCM of 6 and 7 is $42$

Step3: Match constants for elimination

To get $42x$ and $-42x$, multiply first eq by $7$, second by $-6$:
$7*(6x-5y=17) \implies 42x-35y=119$
$-6*(7x+3y=11) \implies -42x-18y=-66$
Adding these cancels $x$ terms.

Answer:

The first equation should be multiplied by 7 and the second equation by -6