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

Answer: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 equationsy = -2x + 3y = x² - 6x +3To 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 +3subtract 3 from both sides-2x =  x² - 6xadd 2x to both sides of the equation0 = x² - 4x0 = x(x - 4)x = 0andx-4 = 0add 4 to both sidesx = 4Now, let´s calculate the y values:y = -2x + 3y = -2 · 0 + 3 = 3y = -2 · 4 + 3 = -5The 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!