how do i solve 10y-3x=-41, 3x-5y=16 using substitution and or elimination?

Question

i need to show my work and check it but i dont even know how to start.   v.v

Answer 1

10y - 3x = - 41      [1]

3x - 5y = 16          [2]

 

So we can rearrange the equation [2] :

3x - 5y = 16

Add 5y to both sides of the equation:

3x - 5y + 5y = 16 + 5y

3x = 16 + 5y

 

We can now substitute this into equation [1] :

So, 10y - 3x = - 41  , becomes:

10y - (16 + 5y) = - 41

10y - 16 - 5y = - 41

5y - 16 = - 41

 

Now add 16 to both sides of the equation:

5y - 16 + 16 = - 41 + 16

5y = - 25

 

Now you can divide both sides of the equation by 5 to find the value of y:

5y/5 = - 25/5

y = - 5

 

You can now substitute this value into either equation [1] or [2]. I will choose [2]:

So,   3x - 5y = 16 ,   becomes:

 

3x - 5(-5) = 16

3x - (- 25) = 16

3x + 25 = 16

Now we can subtract 25 from both sides of the equation:

3x + 25 - 25 = 16 - 25

3x = - 9

 

Now we can divide both sides of the equation by 3:

3x/3 = - 9/3

x = - 3

 

So the solution to the equation is:

x = - 3 and y = - 5