Question

question 9 of 10 10 points
how many real solutions does this system of equations have? $(x - 3)^{2}+(y + 1)^{2}$ $x - 7 = 0$
a 0
b. 3
c 2
d 1

Explanation:

Step1: Solve the linear equation for \(x\)

From \(x - 7=0\), we get \(x = 7\).

Step2: Substitute \(x = 7\) into the circle equation

Substitute \(x = 7\) into \((x - 3)^{2}+(y + 1)^{2}=25\).
We have \((7 - 3)^{2}+(y + 1)^{2}=25\), which simplifies to \(16+(y + 1)^{2}=25\).
Then \((y + 1)^{2}=25 - 16=9\).
Taking square roots, \(y+1=\pm3\).
So \(y=-1 + 3=2\) or \(y=-1-3=-4\).

Answer:

C. 2