Given the following system of equations, what number should you multiply the first equation by so that the x-term will be eliminated when the first equation is added to the second equation?

Question

4x - y + 7z = 65

- 7x + 4y - 2z = - 5

x + 9y - 5z = - 24

-7/4,7/4,4/7,-4/7

Answer 1

7/4

1st equation is

4x-y +7z = 65

2nd equation is

-7x+4y-2z = -5

multiply the 1st by 7/4 gives

7x -7y/4 +49z/4 = 65(7/4)

add to the 2nd equation gives

4y -7y/4 -2z +49z/4 = 65(7/4) -5

with the x eliminated