How do you solve the system of equations by graphing and then classify the system as consistent or inconsistent x + y = 4 and –x + y = 2?

Mar 13, 2016

The equations are consistent.
The point of intersection is $\left(x , y\right) \to \left(1 , 3\right)$

Explanation:

Given:
$x + y = 4$.........................(1)
$- x + y = 2$.....................(2)

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Both equations are in the same format. AS such and the fact that the coefficients of $x$ (which is 1 and -1) are opposite signs then at some point the will coincide. Thus there exists a single pair of coordinates that will satisfy both equations. Consequently they are consistent.

By sight: Directly adding equations (1) and (2) gives:

$2 y = 6$

Thus $y = 3$

Given that $y = 3$, by sight, $x = 1$
So the graphs intersect at $\left(x , y\right) \to \left(1 , 3\right)$

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To graph these write the equations as:
$y = - x + 4$ .............................(1_a)
$y = x + 2$....................................(2_a)

If this is for homework you will be required to produce a table of values for each equation. I would suggest 3 values each