Which of the following steps would you perform to the system of equations below so that the equations have opposite y-coefficients?

4x +2y=4
12x + y=22

a. divide both sides of the top equation by 3
b. divide both sides of the bottom equation by 2
c. multiply both sides of the bottom equation by 3
b. multiply both sides of the top equation by 3

B. divide both sides of the bottom equation by 2

Step-by-step explanation

If opposite means additive inverse, then none of the answers is correct

The given system of equations is

4x+2y=4

12x+y=22

The coefficient of y in the top equation is 2 and the coefficient of y in the bottom equation is 1.

One way to make the coefficient of y have opposite sign is to multiply the bottom equation by -2 to get:

4x+2y=4

-24x-2y=-44

Or we divide the top equation by -2

-2x-y=-2

12x+y=22

If opposite means, multiplicative inverse, then dividing through both sides of the bottom equation by 2 gives:

4x +2y=4

6x + ½y=11

Hence the second choice is correct.

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4