Answer:
The solutions to the system of equations are the points (2, -1) and (-1.2, 0.6)
Explanation:
Hi there!
We have the following system of equations:
x + 2y = 0
x² - 2x + y²- 2y - 3 = 0
The solutions of the system are the pairs (x, y) that satisfy both equations.
Let´s take the first equation and solve it for x:
x + 2y = 0
x = -2y
And now let´s replace the x in the second equation:
x² - 2x + y²- 2y - 3 = 0
(-2y)² -2(-2y) + y² - 2y - 3 = 0
4y² +4y + y² - 2y - 3 = 0
5y² + 2y - 3 = 0
Let´s use the quadratic formula to solve this quadratic equation:
[-b ± √(b² - 4ac)]/2a
a = 5
b = 2
c = -3
The solutions to this equation are:
y = -1 and y = 0.6
The values of x will be:
x = -2y
x = -2(-1) = 2
and
x =-2(0.6) = -1.2
The solutions to the system of equations are the points (2, -1) and (-1.2, 0.6)
Please, see the attached figure. The points where the curves intersect are the solutions of the system.
Have a nice day!