How many solutions are there to the following system of equations?
2x - y = 2
-x + 5y = 3
if this is your question,
there is ONLY 1 way to solve it.
As there is no system of equations shown, there are zero solutions.
Add the two equations together. This will give you a single equation in one variable. Solve this - it should give you two solutions. Then replace the corresponding variable for each of the solutions in any of the original equations.
The system of equations can have zero solutions, one solution, two solutions, any finite number of solutions, or an infinite number of solutions. If it is a system of LINEAR equations, then the only possibilities are zero solutions, one solution, and an infinite number of solutions. With linear equations, think of each equation describing a straight line. The solution to the system of equations will be where these lines intersect (a point). If they do not intersect at all (or maybe two of the lines intersect, and the third one doesn't) then there is no solution. If the equations describe the same line, then there will be infinite solutions (every point on the line satisfies both equations). If the system of equations came from a real world problem (like solving for currents or voltages in different parts of a circuit) then there should be a solution, if the equations were chosen properly.
There are no common points for the following two equations: y = 2x + 3 y = 2x - 1 If you graph the two lines, since they have the same slope, they are parallel - they will never cross.
If the equations or inequalities have the same slope, they have no solution or infinite solutions. If the equations/inequalities have different slopes, the system has only one solution.
It has 2 solutions and they are x = 2 and y = 1 which are applicable to both equations
The answer follows:
There are two solutions and they are: x = -1 and y = 3
The solutions are: x = -2 and y = 4
If a system of equations is inconsistent, there are no solutions.
The equations are identical in value, ie the second is merely twice the first...
The two rational solutions are (0,0,0) and (1,1,1). There are no other real solutions.
Any system of linear equations can have the following number of solutions: 0 if the system is inconsistent (one of the equations degenerates to 0=1) 1 if the system is linearly independent infinity if the system has free variables and is not inconsistent.
As there is no system of equations shown, there are zero solutions.
x - 2y = -6 x - 2y = 2 subtract the 2nd equation from the 1st equation 0 = -8 false Therefore, the system of the equations has no solution.
x = y = 3
They are simultaneous equations and their solutions are x = 41 and y = -58