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.

x = 10.1

step-by-step explanation:

all of the angles of a tirangle add up to 180º

180 - 65 = 115 (since we already know the value of one angle)

(2x + 7) + (8x + 7) = 115

(combins like terms) 10x + 14 = 115

(isolate the variable subtract 14 from both sides): 10x = 101

(find the variable divide both sides by 10): x = 101/10

x = 10.1

3

step-by-step explanation: