Question

How do you solve the system `2x - y = 8`, `x + 2y = 9`?

Answer 1

Solving simultaneous equations involves using algebra to eliminate one variable and solve for the other, then using that one to find the value of the other. The solution is `x=3.33, y=2.33`.

Explanation:

Let's label our two equations as (1) and (2) to make them easy to refer to:

`2x-y=8` (1)
`x+2y=9` (2)

Multiply (2) by 2:

`2x+4y=18`

Subtract (1) from this equation:

`2x+4y=18` minus
`2x-y=8`

Yields:

`3y=10`

This is an equation in only one variable, so we can solve it:

`y=10/3 or 3.33`

Substitute this in either (1) or (2) to find `x`. I'll use (2) because it's simpler:

`x+2(10/3)=9`

Rearranging:

`x=9-20/3 = 2.33`

The solution is `x=3.33, y=2.33`.

(you can check this by substituting these values into either of the two original equations and ensuring that the sides are equal to each other)