Simultaneous Equations

The Basics

Equations with two unknowns are impossible to give a definitive answer on their own, but a more accurate answer can be obtained if two equations are given. For example, you could not solve:

$$2x+4y=36$$

but you could solve these two equations:

$$2x+4y=36$$ $$3x-y=36$$

Solving by Elimination

One way to solve simultaneous equations is to eliminate one of the unknowns from both equations simultaneously if they share a coefficient, then solve the remaining unknown. To remove the unknowns that share a coefficient, you should add if the sign is different and subtract if they have the same sign. With this unknown, you can then solve the other unknown using the first value.

Without Common Coefficients

If there are not common coefficients, multiply the entire equation to have a common coefficient before then solving by elimination. For example:

$$2x+4y=36$$ $$3x-y=36$$

would become:

$$2x+4y=36$$ $$12x-4y=144$$

Solving Garphically

You can solve simultaneous equations graphically. First, to do so, you need to create a table for both equations. Below are the tables for $y=x+1$ and $x+y=5$.

$x$	$-1$	$0$	$1$	$2$	$3$
$y$	$0$	$1$	$2$	$2$	$4$

$x$	$-1$	$0$	$1$	$2$	$3$
$y$	$6$	$5$	$4$	$3$	$2$

Once you have created these tables, they need to be plotted on a graph. The intersection of these will show the values of $x$ and $y$.