3x - y = -4
3x - y = 0
Those lines do not intersect. They are parallel. You can demonstrate by solving either of them for one of the two variables, then plugging it's value into the other:
3x - y = -4
∴y = 3x + 4
Now substitute:
3x - y = 0
∴ 3x - (3x + 4) = 0
∴ 3x - 3x - 4 = 0
∴ -4 = 0
This result is obviously incorrect, indicating that the lines do not intersect.
It works out that they intersect at: (4, -7)
2x^2+3xy-4y2(4)+3(2)(-4)-(4)(-4)8-24+16=0
the north pole is the place where the 2 0 degree lines intersect
x = -1 and y = 2 The lines intersect at (-1, 2)
By graphing the lines on the coordinated plane they will intersect at (2, -4) which is the solution of the equations
By a process of elimination and substitution the lines intersect at: (1/4, 0)
3xy - 3xy = 0
It works out that they intersect at: (4, -7)
By a process of elimination and substitution the lines intersect at: (4, -7)
2x^2+3xy-4y2(4)+3(2)(-4)-(4)(-4)8-24+16=0
the north pole is the place where the 2 0 degree lines intersect
x = -1 and y = 2 The lines intersect at (-1, 2)
By graphing the lines on the coordinated plane they will intersect at (2, -4) which is the solution of the equations
16
When (the graph of the equations) the two lines intersect. The equations will tell you what the slopes of the lines are, just look at them. If they are different, then the equations have a unique solution..
Here's a simple C++ function intersect() that takes four float parameters representing the slopes and y-intercepts of two lines and returns 1 if they intersect, and 0 otherwise: #include <iostream> int intersect(float m1, float b1, float m2, float b2) { // If the slopes are equal, the lines are parallel and do not intersect. return (m1 != m2) ? 1 : 0; } int main() { // Example usage std::cout << intersect(1.0, 2.0, 1.0, 3.0) << std::endl; // Output: 0 std::cout << intersect(1.0, 2.0, -1.0, 3.0) << std::endl; // Output: 1 return 0; } This function checks if the slopes (m1 and m2) of the two lines are equal; if they are, the lines are parallel and do not intersect, returning 0. Otherwise, it returns 1, indicating that the lines intersect.
The simplest answer is y = 0 and x = 0.