The sum of two numbers, x and y, is 12. The difference of four times the larger number and two times the smaller number is 18. Whích system of equations should you use to find the two
numbers?
O
A X-y=12
4x - 2y = 18
O B x + y = 12
X-y= 18
C x+y=12
2x - 4y = 18
D x + y = 12
4% - 2y = 18

D

Step-by-step explanation:

"Sum" indicates that we add the two variables so we can eliminate option A because that has x - y = 12 not x + y = 12. We can eliminate option B because the second equation should be 4x - 2y = 18, not x - y = 18. For that same reason, we can eliminate C because the coefficients are swapped. I will assume that in option D, the second equation is 4x - 2y = 18. Since we have eliminated everything else, the answer is D.

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1