Question

–4x – 7 = y x2 – 2x – 6 = y Which statement is true? There are no real number solutions. There is one unique real number solution at (–1, –3). There is one unique real number solution at (1, –3). There are two real number solutions at (–1, –3) and (1, –7).

Answer 1

Answer:

There is one unique real number solution at (–1, –3)

Step-by-step explanation:

Given the two linear equation

–4x – 7 = y ...1

x² – 2x – 6 = y ...2

Equating the left hand side of both equations since they are equal to the same variable  y will give;

$-4x-7=x^{2} -2x-6\\collecting\ the\ like\ terms\\x^{2} -2x+4x-6+7 = 0\\x^{2} +2x+1 = 0\\x^{2} +x+x+1 = 0\\x(x+1)+1(x+1)=0\\(x+1)^{2}=0\\ taking\ square\ root\ of\ both\ sides\\x+1 = 0\\x = -1$  

Substituting x=1 into equation 1 we have;

$y=-4(-1)-7\\y=4-7\\y = -3$

This means there is only one unique real number solution at (-1, -3)