how to solve each system by elimination 16x-10y=10 and -8x-6y=6

Question

i dont know how to do this

please explain

thanks

Answer 1

Hi again Angelica;

16x-10y=10 and -8x-6y=6

The coefficients of x are 16 and -8. To apply elimination, these should be the same.  Positives and negatives are non-issues.

Let's take the first equation...

16x-10y=10

Let's multiply both sides by 1/2...

(1/2)(16x-10y)=(10)(1/2)

8x-5y=5

Let's add this to the second equation...

-8x-6y=6

8x-5y=5

0-11y=11

The x is eliminated...

-11y=11

Let's divide both sides by -11...

(-11y)/11=11/-11

y=-1

Let's plug this into either original equation to establish the value of x.  I randomly select the second...

-8x-6y=6

-8x-[(6)(-1)]=6

-8x-(-6)=6

Subtracting a negative number is identical to adding a positive number...

-8x+6=6

Let's subtract 6 from both sides...

-8x+6-6=6-6

-8x=0

x=0

Let's plug both values into the first equation to verify results...

16x-10y=10

[(16)(0)]-[(10)(-1)]=10

0-(-10)=10

10=10

 

Answer 2

Solving by elimination with two linear equations can be most easily described as adding the two together. The goal is to eliminate either the x or y variable, then solve for the remaining variable. Since neither coefficient are additive inverses ( 16x + -8x =/= 0), the easiest remedy is to multiple both sides of the second equation by 2.

 

2 (-8x - 6y) = 2(6) results in -16x - 12y = 12

 

Now, add this to the first equation 16x - 10y = 10:

 

     16x - 10y = 10

+  -16x - 12y = 12

=    0x  - 22y = 22

 

Solve for y:

-22y = 22   divide both sides by -22

    y  = -1

 

Now that you know y = -1, substitute it back into the original equation:

16x - 10 (-1) = 10

16x + 10 = 10

16x = 0

  x  = 0

 

To check, substitute x = 0 into the second original equation:

-8 (0) - 6y = 6

-6y = 6

y = -1

 

I hope this is what you were looking for!

Answer 3

see the answers to the prior 4 or 5 questions posed by you on solving by elimination