Question

solve the following pair of linear equation 2x+3y=5 , 7x-5y=2 has a unique solution if yes find the solution

Answer 1

Answer : both x and y = 1

I used elimination method to solve for y then plug y in one of the equation and find for x

Answer 2

(1, 1 )

Explanation:

Given the 2 equations

2x + 3y = 5 → (1)

7x - 5y = 2 → (2)

Multiplying (1) by 5 and (2) by 3 and adding will eliminate the y- term

10x + 15y = 25 → (3)

21x - 15y = 6 → (4)

Add (3) and (4) term by term to eliminate y

31x = 31 ( divide both sides by 31 )

x = 1

Substitute x = 1 into either of the 2 equations and evaluate for y

Substituting into (1)

2(1) + 3y = 5

2 + 3y = 5 ( subtract 2 from both sides )

3y = 3 ( divide both sides by 3 )

y = 1

Solution is (1, 1 )