Question

Find the lines whose combined equation is 6x^2+5xy-4y^2

Answer 1

Answer:

3x + 4y = 0  and  2x - y = 0

Step-by-step explanation:

The lines are given by the points that make the expression equal to zero.

6x² + 5xy - 4y² = 0

<=>  ( 3x + 4y ) ( 2x - y ) = 0

<=>  3x + 4y = 0   or   2x - y = 0.

So the point that make the original expression zero, are precisely the points that make either of the final two expressions zero, so are precisely the points on the lines described by the final two expressions.