Question

- 3x + 3y = 6
x + 3y = 18

solve using substitution
find x and y

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Answer 1

equation 1: - 3x + 3y = 6

equation 2: x + 3y = 18

start with equation 2:

x + 3y = 18

subtract 3y from both sides:

x = 18 - 3y

plug the new equation into equation 1:

- 3x + 3y = 6

- 3 (18 - 3y) + 3y = 6

multiply:

-54 + 9y + 3y = 6

collect like terms:

-54 + 12y = 6

add 54 to both sides, then divide the whole equation by 12:

12y = 60

y = 5

plug the y value into either equation to solve for x. for example, here is equation 2:

x + 3y = 18

x + 3(5) = 18

x + 15 = 18

x = 3

check answer:

x + 3y = 18

3 + 3(5) = 18

3 + 15 = 18

18 = 18 is true

Answer 2

Answer:x = 3 and y = 5

Explanation:

We have two equations:

-3x + 3y = 6 ........(1)

x + 3y = 18 ........(2)

We can use the second equation to solve for y in terms of x:

-4x = -12

x = 4

Now we substitute this expression for y into the second equation:

3 + 3y = 18

3y = 15

y = 5

Therefore, the solution to the system of equations is x = 3 and y = 5.