To eliminate the - 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.

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

Step-by-step explanation:

to solve y we should eliminate x from the equation.

both equations have positive coefficient. 6 and 7. both are positive.

to eliminate 2 positive numbers we should subtract one from the other. but in this question they asked to add 2 equations. so we should multiply one equation with negative value to subtract.

so one equation should be multiplied with positive number and other with negative number.

therefore 2nd and 4th options are wrong

we have to eliminate x from this equation. so when multiply 2 equations with the given number 2 xes should have same value after multiplication but opposite sign

let's do the first option

6x * 3 should be equal to 7x * - 5

18 * is not equal to - 35x

so the answer should be 3rd. but let's check that too

6x * 7 = 7x * - 6

42x = - 42x.

this is the correct one

6x - 5y = 17 * 7

42x - 35y = 119

7x + 3y = 11 * - 6

-42x - 18y = - 66

add both equations

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

-53y = 53

y = (-1)