solving by linear combination

Question

5X+8y=1

3x+4y=1

Answer 1

5x + 8y = 1

3x + 4y = 1

 

Look for the easiest variable to eliminate.

 

If you want to get rid of x, you cam multiple the top equation by 3 and the bottom equation by 5, then subtract the bottom equation from the top.

 

Or

 

get rid of the y terms by multiplying the bottom equation by 2.

 

Remember to multiply both sides of the equation by the same number, not matter which variables you want to eliminate. Also, if you multiply by a negative number to make one equation negative and one positive so you can add instead of subtract, be careful to be consistent with each term.

 

 

Suppose you multiple the bottom equation by -2, then you will get -6x - 8y = -2

 

The system becomes

5x + 8y = 1

-6x - 8y = -2

----------------       now add the two equations

-x = -1                 so x = 1,

 

Plug x =1 into either original equation to find y. Remember y doesn't have to be a whole number.

Answer 2

5x+8y=1
3x+4y=1

 

Multiply the second equation by -2:

 

(-2)*(3x + 4y = 1)

-6x - 8y = -2

 

Now add this to the first equation to eliminate the y variable:

 

 5x + 8y = 1

-6x - 8y = -2

-----------------

 -x  +  0  = -1

 

-x = -1

x = 1

 

To find y, plug x = 1 into either original equation. I'll use 5x+8y = 1

 

5x + 8y = 1

5*1 + 8y = 1

5 + 8y = 1

8y = -4

y = -1/2

 

Check:

5x + 8y = 1
5*1 + 8*(-1/2) = 1

5 + (-4) = 1

1 = 1

 

3x + 4y = 1

3*1 + 4*(-1/2) = 1

3 + (-2) = 1

1 = 1

 

Check!

Answer 3

Multiply the bottom equation by -2.  you get -6x -8y = -2

Add -6x - 8y = -2 to the top equation and you get: -x = -1

Divide both sides by -1 and get x = 1

Plug in to the first equation 5(1) + 8y = 1

Subtract 5 on both sides and get 8y = -4

Divide by 8 and get y = -4/8 = -1/2