Find all solutions to the following system of equations x+2y=0 ; x²-2x+y²-2y-3=0. illustrate with a graph.

The solutions to the system of equations are the points (2, -1) and (-1.2, 0.6)

Step-by-step 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!

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

eventually after a few more steps, your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x

95.03 is the answer. hope this !