Answer :
The solutions of the given system of equations: y = x2 – 7x + 16 and y = x - 1 is 4 + i and 4 - i.
what is quadratic equation?
A quadratic equation in the variable x is an equation of the form
ax² + bx + c= 0, where a, b, c are real numbers, a * 0.
Given equations are:
y= x²-7x+16 and y=x-1
So, x-1= x²-7x+16
or, x²-8x+17=0
or, x²-8x+17 =0
a=1, b=-8, c=17
Using discriminant method,
x= [tex]-b\pm\sqrt{b^{2}-4ac } /2a[/tex]
x= -(-8) ± [√(-8)²- 4*1*17]/2*1
x=8±√(√64-68)/2
x= 8±√(-4)/2
x= 4 ± i
x= 4 + i and x= 4 - i
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