The system of equations has exactly one solution is option A; 2 x + y = 3 and 5x -y = 11.
For that , we will try solving it first using the method of substitution in which we express one variable in other variable's form and then you can substitute this value in other equation to get linear equation in one variable.
If they are coincident(lying over each other), then there will have infinite solution since in that case, they will have infinite points in common.
Thus, if two lines are not in any of above case, they intersect at single point and in that case, the considered system of equation has unique single solution.
We have the following equations;
2 x + y = 3 and 5x -y = 11.
2 x + 2 y = 1 and -2 x - 2 y = 1.
3 x + y = -1 and 6 x + 2 y = -2.
3 x - 2 y = 4 and -3 x + 2 y = 4.
Now, from the first pair of equations;
2 x + y = 3 and 5x -y = 11.
Solving;
2 x + y + 5x -y = 3 + 11
7x = 14
x = 2
Now to find the value of y;
2 x + y = 3
y = -1.
The system of equations has exactly one solution is option A; 2 x + y = 3 and 5x -y = 11.
Learn more about equations here;
https://brainly.com/question/10413253
#SPJ5
