Question

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

Answer 1

k = -5

g = 6

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.

Answer 2

you want to find a common value which will be 15g
3(5g+4k=10)
5(-3g-5k=7)

15g+12k=30
-15g-25k=35
cross out the g and add the rest
-13k=36
k=-5
Then substitute -5 as k into the original equation
5g+4(-5)=10
5g-20=10
5g=30
g=6
So, K=-5 and G=6