How do you solve simultaneous equations?

There are two main methods for solving simultaneous equations. The first method is the elimination method. This method uses addition or subtraction of the two equations with equal amounts of 'x' or 'y' in order to 'eliminate' one of them, so you are only let with one unknown. Once this unknown is found the value can be substituted into an equation to find the second unknown. For example if equation 1 was: 3x+5y=17, and equation 2 was: 3x+3y=5. If you subtract equation 2 from equation 1 (1-2) then you get (3x-3x)+(5y-3y)=(17-5), this simplifies to: 2y=12, so y=6. y=6 can now be substituted into the equation 3x+5y=17, so you'd get 3x+5(6)=17, which simplifies to give 3x=-13, so x=-13/3.The other method for working out simultaneous equations is the substitution method. In this method, you rearrange one of the equations in terms of the unknown, and you substitute this unknown into the other equation. So once an unknown is found it can be resubstitute back into an equation to find the second unknown. For example if equation 1 was: x+2y=12, and equation 2 was: 3x+4y=6. Then equation 1 can be rearranged to give: x=12-2y. This can be substituted into equation 2 as: 3(12-2y)+4y=6, which simplifies to: 36-2y=6, this means that: 2y=30, so y=15. So as x=12-2y, it means that x=12-2(15), which means that x=-18. An extra method for finding simultaneous equations is graphically, by plotting both lines on a graph, and finding the coordinate of the intersection of the lines.