Solve the system of equations by graphing. `x + 2y = 6` `2x + y = 9`

Expert Answers
embizze eNotes educator| Certified Educator

Graph the two lines: since they are given in general form the easiest way is often to find the intercepts.

For x+2y=6 the intercepts are (0,3) and (6,0)

For 2x+y=9 the intercepts are (0,9) and (4.5,0). Since we want to be accurate, it is better to plot lattice points (points with integer coordinates) so we find (3,3) is also on the line.

After graphing (see attachment), it appears that the solution is (4,1).

Check algebraically:

4+2(1)=6

2(4)+1=9

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The solution is (4,1)

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vamkitten | Student

x + 2y = 6

2x + y = 9

x=6-2y

2(6-2y)=9

12-4y=9

3=4y

y=3/4

x=6-2(3/4)

  =6-3/2

  =4.5