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)

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step-by-step explanation: