The point of intersection of the given line and circle is at [tex](0,0)[/tex].
Therefore, the number of solutions of the system of equations = 1.
The coordinate [tex](3,3)[/tex] cannot be a solution to the system of equations because it does not lie on the circle.
The solution of the system of equations is [tex](0,0)[/tex].
What is point of intersection?
To find the point of intersection algebraically, solve each equation for y, set the two expressions for y equal to each other, solve for x, and plug the value of x into either of the original equations to find the corresponding y-value. The values of x and y are the x- and y-values of the point of intersection.
What is solutions of the system of equations?
The solution of a equations is defined as the points, in which the lines represent the intersection of two equations.
[tex](x-2)^{2} + (y+2)^{2} = 8 \\ y = x\\ (y-2)^{2} + (y+2)^{2} = 8 \\\\y^{2} + 4 - 4y + y^{2} + 4 + 4y = 8 \\2y^{2} =0\\y = 0\\x = 0[/tex]
Hence, the graphs intersect at [tex](0,0)[/tex].
Therefore, it is the solution of the equations.
Also, (3,3) does not lie on the circle.
[tex]=(3-2)^{2} + (3+2)^{2}\\ =1^{2} + 5^{2}\\[/tex]
= 26 ≠ 8
Learn more about the solution of system of equations here
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