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

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 $2 x + 3 y = 7 , 3 x + 4 y = 10$?

Solution:

Step 1. Enter the equations.

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

Step 2. Find the lowest common multiple.

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

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

Step 3. Subtract Equation 4 from Equation 3.

[5] $y = 1$

Step 4. Substitute Equation 5 in Equation 1.

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

$x = 2$

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.

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

It checks!

The solution is correct.