Linear Equations in Two Variables — Important Questions

(0, 4), (6, 0), (3, 2)

Check each point: (0,4): 2(0)+3(4)=12 ✓, (6,0): 2(6)+3(0)=12 ✓, (3,2): 2(3)+3(2)=12 ✓, (1,3): 2(1)+3(3)=11 ✗, (2,2): 2(2)+3(2)=10 ✗

True

By definition, a linear equation in two variables ax + by + c = 0 always represents a straight line on the coordinate plane.

2/x + 3/y = 5, 1/(x+1) + 2/(y-3) = 4

First equation: let u = 1/x, v = 1/y gives 2u + 3v = 5. Second equation: let u = 1/(x+1), v = 1/(y-3) gives u + 2v = 4. Other equations contain x² or xy terms.