One solution
2x+y =5
x+2y=4
multiply 1st eq by 2 rhen subtract:
4x+2y = 10
x + 2y = 4
3x = 6
x = 2
plug x into any of the above two equations and solve y = 1
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.
Solve both equations for y, that is, write them in the form y = ax + b. "a" is the slope in this case. Since the two lines have different slopes, when you graph them they will intersect in exactly one point - therefore, there is one solution.
There is no solution for those equations because the lines are parallel so, they never touch.
Infinite.
It works out that the solutions are: x = 3 and y = 2
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.
Each of these have an infinite number of solutions. Never can they be equal.
Solve both equations for y, that is, write them in the form y = ax + b. "a" is the slope in this case. Since the two lines have different slopes, when you graph them they will intersect in exactly one point - therefore, there is one solution.
[x + y = 6] has an infinite number of solutions.
There is no such pair. The solution to equation 1 and equation 2 is x = 1, y = 1. The solution to equation 2 and equation 3 is x = 1, y = 1. And the solution to equation 1 and equation 3 is any point on the line 3x + 2y = 5 - an infinite number of solutions. The fact that the determinant for equations 1 and 3 is zero (or that they are not independent) does not mean that there is no solution. It means that there is no UNIQUE solution. In this particular case, the two equations are equivalent and so have an infinite number of solutions.
-2
Each of the two equations has an infinite number. Simultaneously, they have only one.
Infinite, both equations are equivalent and all possible solutions can be represented on the graph y = 4 - x
There is no solution for those equations because the lines are parallel so, they never touch.
That system of equations has no solution. When the two equations are graphed, they turn out to be the same straight line, so there's no such thing as a single point where the two lines intersect. There are an infinite number of points that satisfy both equations.
There are two solutions and they are: x = -1 and y = 3
x=4y+1 x=4y-1 No,they have different solutions.