Answer:
The system has two solutions:
x₁ = 5 ⇒ y₁ = -10
x₂ = -2 ⇒ y₂ = 11
Explanation:
Let's solve the system of equations, this way:
y = -3x + 5
y = x ² - 6x - 5
Replacing y in the 2nd equation:
y = x ² - 6x - 5
-3x + 5 = x ² - 6x - 5
x ² - 3x - 10 = 0
Solving for x, using the quadratic formula:
(3 +/- √(9 -4 * 1 * -10))/2 * 1
(3 +/- √9 + 40)/2
(3 +/- √49)/2
(3 +/- 7)/2
x₁ = 10/2 = 5
x₂ = -4/2 = -2
x₁ = 5 ⇒ y₁ = -10
x₂ = -2 ⇒ y₂ = 11
As we can see the system has two different solutions