3y=11-2x, 3x=y-11 linear equation solve using the algebraic method check solution

(x, y) = ( - 2, 5)

Step-by-step explanation:

given the 2 equations

3y = 11 - 2x → (1)

3x = y - 11 → (2)

Rearrange (2) expressing y in terms of x

add 11 to both sides

y = 3x + 11 → (3)

Substitute y = 3x + 11 into (1)

3 (3x + 11) = 11 - 2x

9x + 33 = 11 - 2x (add 2x to both sides)

11x + 33 = 11 (subtract 33 from both sides)

11x = - 22 (divide both sides by 11)

x = - 2

Substitute x = - 2 in (3) for corresponding value of y

y = (3 * - 2) + 11 = - 6 + 11 = 5

As a check

substitute x = - 2, y = 5 into (1) and (2) and if the left side equals the right side then these values are the solution.

(1) : left side = (3 * 5) = 15

right side = 11 - (2 * - 2) = 11 + 4 = 15 ⇒ left = right

(2) : left side = (3 * - 2) = - 6

right side = 5 - 11 = - 6 ⇒ left = right

solution = ( - 2, 5)