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;
[tex]-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\\[/tex]
Substituting x=1 into equation 1 we have;
[tex]y=-4(-1)-7\\y=4-7\\y = -3[/tex]
This means there is only one unique real number solution at (-1, -3)
