Question

Y = –1/2x + 4

Answer 1

Answer:  the correct option is (C) No solution.

Step-by-step explanation:  We are given to find the number of solutions to the following system of linear equations :

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

We will try to solve the above system by the method of substitution.

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

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

which can never be possible.

So, the given system of equations will have NO solution.

Option (C) is CORRECT.

Answer 2

Y = -1/2x + 4....sub in -1/2x + 4 in for y in the other equation

x + 2y = -8
x + 2(-1/2x + 4) = -8
x - x + 8 = -8
x - x = -8 -8
0 = -16...incorrect....NO SOLUTIONS