Free Algebra Tutorials!

Try the Free Math Solver or Scroll down to Tutorials!

 Depdendent Variable

 Number of equations to solve: 23456789
 Equ. #1:
 Equ. #2:

 Equ. #3:

 Equ. #4:

 Equ. #5:

 Equ. #6:

 Equ. #7:

 Equ. #8:

 Equ. #9:

 Solve for:

 Dependent Variable

 Number of inequalities to solve: 23456789
 Ineq. #1:
 Ineq. #2:

 Ineq. #3:

 Ineq. #4:

 Ineq. #5:

 Ineq. #6:

 Ineq. #7:

 Ineq. #8:

 Ineq. #9:

 Solve for:

 Please use this form if you would like to have this math solver on your website, free of charge. Name: Email: Your Website: Msg:

# Algebra - Two Variables

## Solving Systems of Equations

For some systems of equations, adding both equations makes it very easy to solve it. However, this works great only on those systems of equations that (ever so conveniently) have terms that cancel out after addition. But what if an unknown doesnâ€™t cancel when you add the equations together?

The trick is to multiply by a constant. Look at your two equations before you add them. Choose one, and figure out what constant to multiply by. Select a constant (it might be negative) such that one unknown will cancel out when you add the equations. Multiply both sides of your chosen equation by the constant, and then add the two equations together.

Example:

x + 4y = 16

2x â€“ y = 5

What are the values of x and y?

Solution:

Look at the equations.

What constant should we use?

 Letâ€™s multiply the second equation by 4: 4(2x â€“ y) = 4 (5) 8x â€“ 4y = 20 Add both equations together: x + 4y = 16 + 8x â€“ 4y = 20 9x + 4y â€“ 4y = 16 + 20 Combine similar terms: 9x = 36 Solve for x: x = 36/9 = 4 Substitute x = 4 to find y: 4 + 4y = 16 4y = 12 y = 12/4 = 3 Check the result with both: 4 + 4(3) = 16 ? Yes! 2(4) â€“ 3 = 5 ? Yes!