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