Question

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

Answer 1

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.