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

one solution: (8, 0)
one solution: (0, 8)
no solution
infinite number of solutions

Respuesta :

texaschic101
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

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 :

[tex]y=-\dfrac{1}{2}x+4~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\\\x+2y=-8~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]

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

[tex]x+2\left(-\dfrac{1}{2}x+4\right)=-8\\\\\\\Rightarrow x-x+8=-8\\\\\Rightarrow 8=-8,[/tex]

which can never be possible.

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

Option (C) is CORRECT.

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