To eliminate the x-terms and solve for y in the fewest steps, by which constants should the equations be multiplied?

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.

The correct answer is:

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

Explanation:

We are told we want to eliminate the x-terms. This means the coefficients should be the same.

It will also be easier if one is positive and one is negative.

The x-coefficient of the first equation is 6 and the x-coefficient of the second equation is 7. In order to have the same coefficients, we should try to make both of them equal 42 (this is the least common multiple, or LCM, of 6 and 7). To do this, multiply the first equation by 7 (6*7 = 42) and the second one by 6 (7*6 = 42). Additionally, to make the second equation negative, we will multiply it by a negative, so -6.

To eliminate the x-terms and solve for y you should:

1. multiply the first equation by 7, then

42x-35y=119;

2. multiply the second equation by -6, then

-42x-18y=-66.

Now you can add the second equation to the first equation:

(42x-35y)+(-42x-18y)=119+(-66),

42x-35y-42x-18y=119-66,

-53y=53,

y=53÷(-53),

y=-1.

correct choice is C.

You can also use option D, then you have to subtract the second equation from the first equation.

horizontal translation of 2 units in the positive x direction

followed by

vertical translation of 3 units in the positive y direction