Question

What is the solution to the system of equations?

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

Answer 1

x = 2, y = -3

or

(2, -3)

Explanation:

6x + 2y = 6

7x + 3y = 5

multiply the first equation by -3 and the second equation by 2 and solve by elimination

6x + 2y = 6

becomes

-18 - 6y = -18

7x + 3y = 5

becomes

14x + 6y = 10

then, add the new equations.

-18x - 6y = -18

14x + 6y = 10

-4x + 0 = -8

-4x = -8

4x = 8

x = 2

then, substitute x for 2 in one of the eqautions.

6x + 2y = 6

12 + 2y = 6

2y = 6 - 12

2y = -6

y = -3