Check if the point (–6, 8) is a point of intersection of the graphs of the system:
x2 + y2 = 100
y = –6
The graph of the given system is shown in the figure.
Find the number of solutions for the system and also estimate the solutions.
How many possible solutions are there for the system of equations graphed?
Find the number of real solutions of the system
9x2 + 25y2 = 225
2x + 3y = 3
by sketching graphs.
x2 – 4y = 0
x – 3y = 3
Graph the system of inequalities.
What are the point(s) of intersection of the line y = x – 2 and the parabola y = 4x2?
Algebraically solve the given system.
Verify the solutions.
The following equations are graphed as shown. Find the exact solutions of the equations algebraically.
x2 + y2 = 25
x2 + 10y2 = 36
Solve the following system of equations.
Find the real solutions of the system.
x2 – y = 6
4x + y = 6
y = x2
x2 + y2 = 20
2x2 – 3y2= 18
x2 + y2 = 19
Work out the points of intersection, if any, of the graphs in the system.
x2 – y2 – 6x + 6y – 18 = 0
x2 + y2 – 6x – 6y + 18 = 0
4x2 + 5y2 = 69
–x + y = –3
xy + 12 = 0
Solve the equations algebraically.
x = y
Find the points, if any, that the graphs of all three equations have in common.
x2 + y2 – 6 = 0
x2 + y2– 4x + y = 0
3x2 + 3y2– 7x – 14 = 0
x2 + y2 – 5x – 5y = 30
x2 + y2– 5x = 70
y = 3x – 10
Solve the inequality graphically.
x2 + y2 9
x2 + y2 49
(y – 5)2 x + 3
x2 y + 6
Find the square root of the complex number 21 + 20i.
Find the square root of the complex number –15 + 8i.
The sum of the two numbers is 15 and the sum of their squares is 125. Find the two numbers.
The perimeter of a rectangle is 62 ft and the length of its diagonal is 25 ft. Find the dimensions of the rectangle.
Find the point on the circle x2 + y2 = 1 that is closest to the point (3, 4).
