Question

Solve the system of equations using row operations. Write your answer in the form (x, y).

{2x+3y=-2
{3x-y=19

Answer 1

(5, - 4 )

Explanation:

Given the 2 equations

2x + 3y = - 2 → (1)

3x - y = 19 → (2)

Multiplying (2) by 3 and adding to (1) will eliminate the y- term

9x - 3y = 57 → (3)

Add (1) and (3) term by term to eliminate y

(2x + 9x) + (3y - 3y) = (- 2 + 57), that is

11x = 55 ( divide both sides by 5 )

x = 5

Substitute x = 5 into either of the 2 equations and solve for y

Substituting into (1)

2(5) + 3y = - 2

10 + 3y = - 2 ( subtract 10 from both sides )

3y = - 12 ( divide both sides by 3 )

y = - 4

Solution is (5, - 4 )