Question

How do you solve $ x + y = 4 $ and $ x - y = 2 $ by graphing?

Answer 1

Hint: In order to solve the equation’s make two graphs separately by taking one equation at a time. Writing the equation in the form of others and making a table. Mark the points and make the line. Similarly draw the line for the other too. The point where the two lines meet will be the answer for the two equations.

Complete step-by-step answer:
We are given the two equations that are: $ x + y = 4 $ and $ x - y = 2 $ .
Taking the first equation $ x + y = 4 $ , write it in terms of any variable, and we get:
 $ y = 4 - x $
Making a table of the points by taking any random value of $ x $ , putting it in the equation and getting $ y $ .
The table obtained from this method for at least 5 values is:

x	0	1	2	3	4
y	4	3	2	1	0

Mark these points in the graph.
Similarly for the other equation that is $ x - y = 2 $ , writing it in terms of any variable, and we get:
 $ y = x - 2 $
Making a table of the points by taking any random value of $ x $ , putting it in the equation and getting $ y $ .
The table obtained from this method for at least 5 values is:

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

Marking these points in the graph and we get two lines in the graph. The point where the two points are intersecting is the answer of the equations:
The graph obtained is:

From the graph we can see that the two lines are intersecting at $ \left( {3,1} \right) $ .
Therefore, the Answer of the two equations $ x + y = 4 $ and $ x - y = 2 $ after solving by graphing is $ \left( {3,1} \right) $ .

Note: We can check the value by putting the point obtained in any one of the equations given above, if it results the same then it is correct.
We can also solve the equation using substitution or elimination methods.