How do you solve a system of equations by using the elimination method?

1 Answer
Aug 16, 2015

You follow a sequence of steps.

In general, the steps are:

  1. Enter the equations.
  2. Multiply each equation by a number to get the lowest common multiple for one of the variables.
  3. Add or subtract the two equations to eliminate that variable .
  4. Substitute that variable into one of the equations and solve for the other variable.
  5. Check by substituting your answer into one of the equations,

EXAMPLE:

How do you use the elimination method to solve #2x+3y=7, 3x+4y=10#?

Solution:

Step 1. Enter the equations.

[1] #2x+3y=7#
[2] #3x+4y=10#

Step 2. Find the lowest common multiple.

Multiply Equation 1 by #3# and Equation 2 by #2#.

[3] #6x+9y =21#
[4] #6x+8y=20#

Step 3. Subtract Equation 4 from Equation 3.

[5] #y=1#

Step 4. Substitute Equation 5 in Equation 1.

#2x+3y=7#
#2x+3=7#
#2x=4#

#x=2#

Check: Substitute the values of #x# and #y# in Equation 2.

If you use one equation to get the second variable, use the other equation for the check.

#3x+4y=10#
#3×2+4×1=10#
#6+4=10#
#10=10#

It checks!

The solution is correct.