I have to solve the linear system. What is the linear system when y=3/4x+8 and 4y=3x+4

Question

Solve the Linear system

y=3/4x+8

4y+3x+4

Answer 1

The 1st equation is y = (3/4)x + 8  

 

The 2nd equation is 4y = 3x + 4  ==>  y = (3/4)x + 1  

 

If you graph these 2 lines you will see that they are parallel (they have the same slope but different y-intercepts) so they will never cross, which means that there is no solution to this linear system.  

 

You can get this result algebraically by subtracting the second equation from the 1st, which will leave you with 

 

0*y = 0*x + 7 

0 = 7 

 

which is always a false statement, so it cannot be true for any values of x and y, which means that there is no solution to this linear system.