SOLVING SIMULTANEOUS EQUATION : Solving by Elimination Method

How to solve - Solving Simultaneous Equation : Solving by Elimination Method?

1. Group the equations into first (1) and second (2) equations. 
2. Two equations are simplified by adding or subtracting them.
3. This eliminates one of the variables so that the other variable can be found. 
4. Find the other variable by substituting the first variable to either the two original equations

Examples : Solving Simultaneous Equation by Elimination method.

EXAMPLE 1 $\begin{array}{l}7a-2b=26\\ 6a+5b=29\end{array}$
Step (1) Group the equations into first (1) and second (2) equations.	$\begin{array}{l}7a-2b=26\to \left(1\right)\\ 6a+5b=29\to \left(2\right)\end{array}$
Step (2) Two equations are simplified by adding or subtracting them. Step (3) This eliminates one of the variables so that the other variable can be found.	$\begin{array}{l}\left(1\right)\times 6\\ 42a-12b=156\to \left(3\right)\\ \left(2\right)\times 7\\ 42a+35b=203\to \left(4\right)\\ \\ \left(3\right)-\left(4\right)\\ \left|\begin{array}{c}42a\\ 42a\end{array}\right|\left|\begin{array}{c}-12b\\ +35b\end{array}\right|\begin{array}{c}=\\ =\end{array}\left|\begin{array}{c}156\\ 203\end{array}\right|\\ \left|-12b-35b\right|=\left|156-203\right|\\ -47b=-47\\ b=1\end{array}$
Step (4) Find the other variable by substituting the first variable to either the two original equations	Substitute b = 1 into (1) $$\begin{array}{l}7a-2\left(1\right)=26\\ 7a=26+2\\ 7a=28\\ a=\frac{28}{7}\\ a=4\end{array}$$

EXAMPLE 2 $\begin{array}{l}x+2y=-1\\ 4x-3y=18\end{array}$
Step (1) Group the equations into first (1) and second (2) equations.	$\begin{array}{l}x+2y=-1\to \left(1\right)\\ 4x-3y=18\to \left(2\right)\end{array}$
Step (2) Two equations are simplified by adding or subtracting them. Step (3) This eliminates one of the variables so that the other variable can be found.	$\begin{array}{l}\left(1\right)\times 4\\ 4x+8y=-4\to \left(3\right)\\ 4x-3y=18\to \left(2\right)\\ \\ \left(3\right)-\left(2\right)\\ \left|\begin{array}{c}4x\\ 4x\end{array}\right|\left|\begin{array}{c}+8y\\ -3y\end{array}\right|\begin{array}{c}=\\ =\end{array}\left|\begin{array}{c}-4\\ 18\end{array}\right|\\ \left|8y-3y\right|=\left|-4-18\right|\\ \\ 11y=-22\\ y=\frac{-22}{11}\\ y=-2\end{array}$
Step (4) Find the other variable by substituting the first variable to either the two original equations	$\begin{array}{l}x+2\left(-2\right)=-1\\ x-4=-1\\ x=-1+4\\ x=3\end{array}$

Try it yourself - Solving Simultaneous Equation by Elimination method

$\begin{array}{l}x+y=7\\ x-y=3\end{array}$	$$x=5,y=2$$
$\begin{array}{l}2x+5y=7\\ x+3y=4\end{array}$	$$x=1,y=1$$
$\begin{array}{l}3x+2y=12\\ 4x-y=5\end{array}$	$$x=2,y=3$$
$\begin{array}{l}5x-3y=11\\ 3x+y=8\end{array}$	$$x=2.5,y=0.5$$
$\begin{array}{l}5x=2y\\ 3x+7y=41\end{array}$	$$x=-2.83,y=-7.07$$
$$\begin{array}{l}3x-2y=13\\ 2x+5y=-4\end{array}$$	$$x=3,y=-2$$
$$\begin{array}{l}5x=1-3y\\ 2x+y+4=0\end{array}$$	$$x=-13,y=22$$

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