Question

y= -1/2x + 4
x + 2y=–8
How many solutions does this linear system have?

A.) one solution: (8, 0)
B.) one solution: (0, 8)
C.) no solution
D.) infinite number of solutions

Answer 1

c) No solution. If you plug in y=-1/2x+4 into the y for x+2y=-8. You can see that there is no solution. 

Answer 2

Answer:  The correct option is (C). no solution.

Step-by-step explanation:  The given system of linear equations is

$y=-\dfrac{1}{2}x+4~~~~~~~~~~~~~~~~~~~~(i)\\\\x+2y=8~~~~~~~~~~~~~~~~~~~~~~~(ii)$

We are given to find the number of solutions that the above system have.

Let us try to solve the given system of equations.

Substituting the value of 'y' from equation (i) in equation (ii), we ave

$x+2\left(-\dfrac{1}{2}x+4\right)=-8\\\\\\\Rightarrow x-x+8=-8\\\\\Rightarrow 8=-8\\\\\Rightarrow 16=0,$

which is never true.

So, the system of equations have no solution.

Thus, (C) is the correct option.