# How do you solve the system x+y=6 and x-y=2 by graphing?

Jun 24, 2016

The common point ( point of intersection) is: $\left(x , y\right) \to \left(4 , 2\right)$

#### Explanation:

Simultaneous equations are such that (normally) they plot a range of value that are different to each other. That is, until they cross . At that instant the both have the same values for $x \text{ and } y$. They must have to be able to 'occupy' the same point. For some equation types it can be more than one point and for others, no point at all.

$\textcolor{b l u e}{\text{To determine value of } x}$

Write as:

$x + y = 6$
$\underline{x - y = 2} \text{ "larr" add to and up with only 1 unknown}$
$2 x + 0 = 8$

Divide both sides by 2

Thus $x = 4$
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$\textcolor{b l u e}{\text{To determine value of } y}$

Substitute $x = 4$ into $x + y = 6 \text{ }$giving:

color(brown)(x+y=6) " "color(blue)(->" "4+y=6)

Subtract 4 from both sides

$\textcolor{b r o w n}{4 \textcolor{b l u e}{- 4} + y = 6 \textcolor{b l u e}{- 4}}$

$0 + y = 2$

$y = 2$
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