Solving a pair of equations simultaneously means finding values for the variables (typically
\( x \) and \( y \)) which satisfy both equations at the same time.
We can't solve an equation if it involves two unknown variables. For example, the equation
\[ x+y=6 \]
has lots of possible solutions (0 + 6, 1 + 5 and so on).
But if we have a pair of equations involving two unknown variables, we can often eliminate one of the variables if we 'combine' the equations by either adding them together or subtracting one from the other.
The trick is to make sure that you have either the same number of \( x \)'s or \( y \)'s in both equations, and then:
If you do that correctly, you will be left with one equation involving only one variable, which you will be able to solve for.
Finally, substitute the value you obtain for one of your variables into one of the original equations in order to find the value of the second variable.
You can check your answer by substituting the values you find into each of the original equations - they should satisfy both equations.