Find all solutions to the following system of equations y=-2x+3 ; y=x²-6x+3.illustrate with a graph.

The solutions of the system are the points (0, 3) and (4, -5)

Step-by-step explanation:

Hi there!

First, let´s write the system of equations

y = -2x + 3

y = x² - 6x +3

To solve the system, we have to find the pairs (x,y) that satisfy both equations. So, let´s equalize both equations and solve the resulting equation for x.

-2x + 3 = x² - 6x +3

subtract 3 from both sides

-2x =  x² - 6x

add 2x to both sides of the equation

0 = x² - 4x

0 = x(x - 4)

x = 0

and

x-4 = 0

add 4 to both sides

x = 4

Now, let´s calculate the y values:

y = -2x + 3

y = -2 · 0 + 3 = 3

y = -2 · 4 + 3 = -5

The solutions of the system are the points (0, 3) and (4, -5)

Please, see the attached graphic. The points where the two curves intersect are the solutions of the system.

Have a nice day!

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answer:   y=2x-3

step-by-step explanation: