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y = -2/3x+1 (1)
2x + 3y = 9 (2)
Multiply equation (1) by 3 and write it in the standard form. Then you will get the system in this equivalent form
2x + 3y = 1, (1')
2x + 3y = 9. (2')
The left sides of these equations are identical, while the right sides are different.
Hence, the system does not have solutions.
The equations represent two parallel straight lines that have no intersection (common points).
It is the geometric interpretation of the situation.
For more info see the lesson
- Geometric interpretation of a linear system of two equations in two unknowns
in this site.
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