–2х + 4y = 1
3х – бу = 9
how many solutions does this system have

No solutions, 0 solutions

Step-by-step explanation:

The number of solutions a linear system has depends on the slope of the lines, and if the lines are equivalent. The information is easiest to find in slope-intercept form y = mx + b.

"m" is the slope.

"b" is the y-intercept.

"x" and "y" are points on the line.

Remember a solution is the point of intersection, or meeting point of the lines when graphed.

Situations for the number of solutions for linear systems:

Infinite solutions - Equivalent equations. When two lines are actually the exact same when you graph them, they will have an infinite number of solutions. You can determine if two equations are equivalent by making them equal each other, then substituting a random "x" value. If lines have the same "m" and "b" value, they are equivalent.

No solutions - Same slope, different y-intercepts. When two equations have the same slope (and they are not the same equation) they are parallel. When lines are parallel, they never meet. If lines never meet, there cannot be a solution.

One solution - different slopes, different y-intercepts. In slope-intercept form, when the values for "m" and "b" in the two equations are different, the system will have one solution.

Convert the two equations to slope-intercept form y = mx + b by isolating "y". To isolate, move all other numbers to the other side of "y". When you move a number, you do the opposite operation (The opposite of addition is subtraction. The opposite of multiplication is division.)

-2x + 4y = 1

4y = 2x + 1

y =

y =

m = 1/2   b = 1/4

3x - 6y = 9

-6y = -3x + 9

y =

y =

m = 1/2   b = -3/2

The two equations have the same slope, different y-intercepts Therefore, there are no solutions because they are parallel and will never meet.

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Explanation: