Question

how can i determine if a linear system has infinite number of solution, only one, or none?
example:
14x + 7y = 315
16x - 2y = 610

Answer 1

Solve the system. If the system is unable to be solved, it has no solution. If the system results in the same equation on both sides, it has infinite solutions. If there is one x value or one y value, it has one solution.

Answer 2

I think the point of the question was to know before you solve it :)
If one equation is an exact multiple of another, you have infinite solutions. If the coefficients in one equation are multiples of the coefficients in another, but the constants are not, then you have no solutions. Otherwise, you have one.

Answer 3

Solve for y.
in the form of y=mx+b
If the have same solve but different y int it means no Solution.. means they will next cut each other.
On the Other hand, if ewe have same slope and same y int, it means we will have lines on each other, so infinte number of solutions.
If they have different slope and diffrnt y-int means 1 solution.

Answer 4

Examples:
Infinite number of solutions:
\[ 3x + 2y = 1\]
\[ 9x + 6y = 3\]
No solutions:
\[7x - y = 4\]
\[14x - 2y = 9\]
One solution:
\[2x - y = 4\]
\[4x - y = 2\]