Need help with these equations: x+3y=11 and 2x-y=1

Question

Having trouble coming up with two variables.

Answer 1

x+3y=11 and 2x-y=1

 

There are two standard ways to solve this pair of equations, substitution and linear combination.

 

Substitution:

x+3y=11

2x-y=1

 

Rewrite the second equation solving for x:

 

2x = y + 1

x = (1/2)y + (1/2)

 

Substitute (1/2)y + (1/2) for x in the first equation:

x+3y=11

(1/2)y + (1/2) +3y = 11

(7/2)y = 21/2

 

y = 3

 

Find x: x = (1/2)y + (1/2) = (1/2)(3) + (1/2) = 3/2 + 1/2 = 2

 

x=2

 

Linear Combination:

x+3y=11
2x-y=1

 

Multiply the first equation by -2

 

-2x -6y = -22

 

Now add it to the second equation to eliminate the x terms:

 

-2x - 6y = -22

 2x  -  y =    1

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

  0   - 7y = -21

 

y = 3

 

Find x: x = 11 - 3y = 11 - (3)(3) = 2

 

x=2