Solve the system of equations algebraically.
5g+4k=10
-3g-5k=7

k = -5

g = 6

Step-by-step explanation

1) First solve for k and plug that into the other equation to solve for g.

5g + 4k = 10

4k = -5g + 10

k = -5/4g + 2.5

2) Plug k into the other equation to solve for g

-3g - 5k = 7

-3g = 5k + 7

-3g = 5(-5/4g + 2.5) + 7         Use the distributive property

-3g = -6.25g + 12.5 + 7        Combine like terms and simplify

-3g = -6.25g + 19.5               Add 6.25g to both sides

3.25g = 19.5                          Divide 3.25 from both sides to find g

g = 6

3) Now we take this g and plug it into the other equation to find k

(we could also just plug it into this equation as well)

5g + 4k = 10

5(6) + 4k = 10

30 + 4k = 10

4k = -20

k = -5.

If we really wanted to doube check this then we could plug the k value into the equation we used to find the g value...

-3(6) - 5(-5) = 7

-18 + 25 = 7

So yes, k = -5 and g = 6.

b is the final answer! : )