to eliminate the x terms and solve for y in the fewest steps, by which constants should the equations be…

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?\nfirst equation: 6x - 5y = 17\nsecond equation: 7x + 3y = 11\nthe first equation should be multiplied by 3 and the second equation by -5.\nthe first equation should be multiplied by 3 and the second equation by 5.\nthe first equation should be multiplied by 7 and the second equation by -6.\nthe first equation should be multiplied by 7 and the second equation by 6.

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?\nfirst equation: 6x - 5y = 17\nsecond equation: 7x + 3y = 11\nthe first equation should be multiplied by 3 and the second equation by -5.\nthe first equation should be multiplied by 3 and the second equation by 5.\nthe first equation should be multiplied by 7 and the second equation by -6.\nthe first equation should be multiplied by 7 and the second equation by 6.

Answer

Explanation:

Step1: Recall elimination - method goal

To eliminate the $x$ - terms, we want the coefficients of $x$ in both equations to be additive inverses. The coefficient of $x$ in the first equation is $6$ and in the second equation is $7$.

Step2: Analyze the products

If we multiply the first equation $6x - 5y=17$ by $7$, we get $42x-35y = 119$. If we multiply the second equation $7x + 3y=11$ by $- 6$, we get $-42x-18y=-66$. When we add these two new - equations together, the $x$ - terms ($42x$ and $-42x$) will cancel out.

Answer:

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