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The solution to the system of equations 2x - 5y = 6 and -3x + 2y = 13 is also a solution to the equation kx-3y = 10. Find the value of k.

Sagot :

Answer:

2/7

Let me know if it's right btw. I'm not that sure.

Step-by-step explanation:

Let's disregard the kx -3y = 10 part.

We will use this part later to check our answer.

2x - 5y = 6

-3x + 2y = 13

Let's eliminate. Multiply the top equation by 2.  

2(2x-5y) = 2(6) = 4x-10y=12

Multiply the bottom equation by 5

5(-3x +2y) = 5(13) = -15x + 10y = 65

-15x + 10y = 65

4x-10y=12

Let's add the equations to cancel the y's.

-11x = 77

Divide both sides by -11

x = -7

Let's plug -7 back in to one equation to find y.

2(-7) - 5y = 6

-14 - 5y = 6

Add 14 to both sides and you get -5y=20

y = -4

(-7,-4) is our solution BUT WE AREN'T DONE! We need to find k.

Plug in the x and y value (-7 is our x value and -4 is our y value)

-7k + 12 = 10

subtract 12 from both sides and you get -7k = -2

divide both sides by -7 and you get k =2/7!

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