what i need answered

Question

Solve the system 8x - 6y = -20 and -16x + 7y = 30. Write your answer as a coordinate point

Answer 1

Solve the system 8x - 6y = -20 and -16x + 7y = 30. Write your answer as a coordinate point.

Since we want to find terms that drop out or subtract, multiply both sides of the first equation by 2 and add the resulting equation to the second equation.

Change 1st equation: 2(8x-6y) = 2(-20) ⇒ 16x - 12y = -40

Add the like terms of both equations together:

16x - 12y = -40

-16x +7y = 30

0 - 5y = -10

Solve for y by dividing both sides by -5

-5y/-5 = -10/-5

y = 2

Plug the value of y into one of the equations to find x

-16x + 7(2) = 30 ⇒ -16x + 14 = 30 ⇒ -16x + 14 (-14) = 30 (-14)

⇒ -16x + 0 = 16

-16x/-16 = 16/-16 ⇒ x = -1

The coordinate point is (x, y) in this case: (-1, 2)

Answer 2

multiplies first equation by 2, the system is:

16x - 12y = -40

-16x + 7y = 30

Adds them together:

-5y = -10

y = 2

Substitutes:

16x - 12(2) = -40 ---> 16x - 24 = -40 ---> 16x = -16 ---> x = -1

-16x + 7(2) = 30 --> -16x + 14 = 30 --> -16x = 16 --> x = -1

the solution is (-1,2)