Phyllis D.

asked • 04/13/14
# Need help with these equations: x+3y=11 and 2x-y=1

Having trouble coming up with two variables.

Philip P.
answered • 04/13/14

Affordable, Experienced, and Patient Algebra Tutor

*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**

## Still looking for help? Get the right answer, fast.

#### OR

Find an Online Tutor Now
Choose an expert and meet online.
No packages or subscriptions, pay only for the time you need.