how do I create a system of two linear equations that has (3,4) as the only solution? (Part B)infinitely many solutions? (Part C) the empty set solution?

Question

i need to know how to create two linear equation that has (3,4) as the only solution. 

Answer 1

Part 1)

 

You will have two equations in which when you plug in x=3 and y=4 into both of them, the equations are satisfied.

 

x + y = 7               

 

2x + 3y = 18         

 

 

Part 2)

 

Since the equations have finite solutions, the two linear equations will be the same.  This means that any point that lies on this line is a solution.

 

x + y = 5

 

x + y = 5

 

 

Part C)

 

To have an empty set of solutions, the equations must have the same slope, but have different y-intercepts.  This lines are parallel to each other and will never intersect.  Also, the values of x and y do not satisfy the equations.

 

x + y = 2

 

x + y = 4