Answer:
see explanation
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = 2 and c = - 2, thus
y = 2x - 2 ← equation of line
Hence system of equations is
y = x² - x - 6 → (1)
y = 2x - 2 → (2)
Since both equations express y in terms of x we can equate the right sides
x² - x - 6 = 2x - 2 ( subtract 2x - 2 from both sides )
x² - 3x - 4 = 0 ← in standard form
(x - 4)(x + 1) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 4 = 0 ⇒ x = 4
x + 1 = 0 ⇒ x = - 1
Substitute these values into (2) for corresponding values of y
x = 4 : y = (2 × 4) - 2 = 8 - 2 = 6 ⇒ (4, 6 )
x = - 1 : y = (2 × - 1) - 2 = - 2 - 2 = - 4 ⇒ (- 1, - 4 )
Solutions to the system of equations are
(- 1, - 4 ) and (4, 6 )
Answer:
The answer to your question is below
Step-by-step explanation:
Data
Parabola y = x² - x - 6
Line slope = 2 and y- intercept = -2
Process,
Write the equation of the line,
y = mx + b
m = 2
b = -2
y = 2x - 2
To solve this system of equations equal both "y" to have only one equation in terms of "x".
2x - 2 = x² - x - 6
Equal to zero
x² - x - 6 - 2x + 2 = 0 and simplify
x² - 3x - 4 = 0
Solve the quadratic equation by factoring
(x -4)(x + 1) = 0
Find the x values
x₁ = 4 and x₂ = -1
Finally find the y values
y₁ = 2(4) - 2 = 8 - 2 = 6
y₂ = 2(-1) - 2 = -2 - 2 = -4
Give the result
P₁ (4, 6) P₂ (-1, -4)
