Solve the system of equations

6x+7y = 5 2x-3y = 7

The solution is (2, - 1)

Step-by-step explanation:

* You have two ways to solve the system of equations

1. Elimination method:

By making the coefficients of one of the two variables equal in the 2

equations in magnitude and different in sign to eliminate it and find the

other variable

2. Substitution method:

By finding one of the two variables in terms of the other in one of the

two equations and substitute this value in the second equation

* Lets solve our system using the elimination method

∵ 6x + 7y = 5 ⇒ (1)

∵ 2x - 3y = 7 ⇒ (2)

- Multiply equation (2) by - 3 to eliminate x

∵ (-3) (2x) - (-3) (3y) = (-3) (7)

∴ - 6x + 9y = - 21 ⇒ (3)

- Add equation (1) and (3)

∴ 7y + 9y = 5 + - 21

∴ 16y = - 16

- Divide each side by 16

∴ y = - 1

- Substitute the value of y in equation (1)

∴ 6x + 7 (-1) = 5

∴ 6x - 7 = 5

- Add 7 to both sides

∴ 6x = 12

- Divide both sides by 6

∴ x = 2

* The solution is (2, - 1)