Solve the system using elimination

2x+3y=9

x+5y=8

What is the solution?

(x, y) = (3, 1)

Step-by-step explanation:

given the 2 equations

2x + 3y = 9 → (1)

x + 5y = 8 → (2)

multiplying (2) by - 2 then adding to (1) will eliminate the term in x

multiply (2) by - 2

- 2x - 10y = - 16 → (3)

add 1 (1) and (3) term by term

(2x - 2x) + (3y - 10y) = (9 - 16)

- 7y = - 7 (divide both sides by - 7)

y = 1

Substitute y = 1 in either (1) or (2) and solve for x

(1) : 2x + 3 = 9 (subtract 3 from both sides)

2x = 6 (divide both sides by 2)

x = 3

Solution is (3, 1)