Type the correct answer in the box use/ for the fraction bar y=x^2-2x-19 y+4x=5 the pair of the points representing the solution set of the system of equation is (-6,29) and

see explanation

Step-by-step explanation:

given the 2 equations

y = x² - 2x - 19 → (1)

y + 4x = 5 → (2)

substitute y = x² - 2x - 19 into (2)

x² - 2x - 19 + 4x = 5 ( subtract 5 from both sides )

x² + 2x - 24 = 0 ← in standard form

(x + 6)(x - 4) = 0 ← in factored form

equate each factor to zero and solve for x

x + 6 = 0 ⇒ x = - 6

x - 4 = 0 ⇒ x = 4

substitute each value of x into (1) for corresponding y- coordinate

x = - 6 : y = (- 6)² - 2(- 6) - 19 = 36 + 12 - 19 = 29 ⇒ (- 6, 29)

x = 4 : y = 4² - 2(4) - 19 = 16 - 8 - 19 = - 11 ⇒ (4, - 11)

the solutions are (- 6, 29), (4, - 11)

the equation of the parallel line would be y = 2x + 9

step-by-step explanation:

to start we need to find the slope of the original line. we can do that by looking at the coefficient of x, which is 2

since the slope of the original line is 2 and parallel lines have the same slope, we know the new line will also have 2 slope. now we can use that along with the point given in point-slope form to get the find equation.

y - y1 = m(x - x1)

y - 5 = 2(x + 2)

y - 5 = 2x + 4

y = 2x + 9