A system of equations are shown below
-y+2x=4
2x-y= -4
if i solve separately it has infinite solutions
but if i solve together there are no solutions
is it infinite or no solution?
What do you mean "solve it separately" ? It's a system. If you rearrange things to match, you have
2x-y = 4
2x-y = -4
Clearly there are no solutions; the lines are parallel, and do not intersect.
Two parallel lines never cross, no solution.
y = 2 x - 4
y = 2 x + 4
In this case, since you mentioned that solving the system of equations separately (i.e., using elimination or substitution) leads to infinite solutions, and solving it together (likely using elimination) results in no solution, we can conclude that the system has no solution.
When solving a system of equations, it's important to verify whether the resulting equations are valid solutions for both original equations. In this situation, when you obtained an infinite number of solutions when solving the individual equations, it indicates that the two original equations are essentially the same. However, when you tried to solve them together and no solution was found, it suggests that the equations are contradictory or inconsistent, and therefore cannot be satisfied simultaneously.
In this case, the system of equations appears to be inconsistent, meaning there are no solutions that satisfy both equations simultaneously. Let's analyze the situation to understand why.
First, let's solve the system of equations individually to see what results we get:
1) -y + 2x = 4
Rearranging the equation, we get: 2x - y = 4. Notice that this equation is equivalent to the second equation in the system.
2) 2x - y = -4
This equation is the same as the second equation provided in the system.
As you can see, both equations represent the same line. Therefore, when you solve each equation individually, you obtain an infinite number of solutions because any point on the line satisfies the equation.
However, if you try to solve the system of equations together, you will notice that the equations contradict each other. By subtracting one equation from the other, we get:
(2x - y) - (2x - y) = 4 - (-4)
0 = 8
Here, we end up with a contradictory statement: 0 is not equal to 8. This implies that there are no values for x and y that satisfy both equations simultaneously.
In summary, while solving the equations individually results in an infinite number of solutions (because the equations represent the same line), when solved together, the system has no solutions at all because the equations contradict each other.
Therefore, the correct conclusion is that this system of equations has no solution rather than an infinite number of solutions.