Simultaneous equations part three

Equations and graphs Simultaneous equations part three

Another way to solve simultaneous equations is through elimination. Elimination is the process of getting rid of something.

Seeing as we have started by giving examples from a spy thriller we might find a sentence using this word from our make-believe novel. “I suspected her of eliminating him by putting poison in his tomato soup.”

In simultaneous equations, we need to eliminate either the $x$ or the $y$ from one of the equations. We can do this by rearranging and adding or subtracting the equations. Here is an example:

$5x + 3y = 7$		(1)
$3x - y = 7$		(2)
$9x - 3y = 21$	(2) $\times 3$	(3)
$5x + 3y + 9x - 3y= 7 + 21$ $14x = 28$ $x = \frac{28}{14}$ $x = 2$	(3) $+$ (1)	(4)
$5x + 3y = 7$ $5 \times 2 + 3y = 7$ $10 + 3y = 7$ $3y = -3$ $y = -1$	sub (4) into (1)	(5)
$3x - y = 7$ $3 \times 2 + 1 = 7$ $6 + 1 = 7$ $7 = 7$	sub (4) and (5) into (2)	(6)

We did some rearranging in step (3), elimination happened in step (4). $y$ was eliminated and we solved the equation for $x$ . In step (5) we found $y$ . In (6) we did a check to make sure we have the right values for $x$ and $y$ .

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