What are the solutions to the system of equations?

{y=2x2−8x+5
{y=x−2

The solutions of the system of equations are (1 , -1) and ( ,   )

Step-by-step explanation:

The system of equations has a quadratic equation and a linear equation to solve it equate the two equations to find the values of x and then find the values of y

∵ y = 2x² - 8x + 5 ⇒ (1)

∵ y = x - 2 ⇒ (2)

- Equate (1) and (2)

∴ 2x² - 8x + 5 = x - 2

- Subtract x from both sides

∴ 2x² - 9x + 5 = - 2

- Add 2 to both sides

∴ 2x² - 9x + 7 = 0

Let us factorize it into two factors

∵ 2x² = (2x)(x)

∵ 7 = (7)(1)

- The last sign in the trinomial is (+) and the middle sign is (-)

   then the two factors have (-) middle signs

∵ (2x)(1) + (x)(7) = 2x + 7x = 9x ⇒ nears and extreams

∴ The factors of 2x² - 9x + 7 are (x - 1)and (2x - 7)

∴ (x - 1)(2x - 7) = 0

Equate each factor by 0 to find x

∵ x - 1 = 0

- Add 1 to both sides

∴ x = 1

∵ 2x - 7 = 0

- Add 7 to both sides

∴ 2x = 7

- Divide both sides by 2

∴ x =

Now substitute the values of x in equation (2) to find the values of y

∵ x = 1

∴ y = 1 - 2 = -1

∵ x =  

∴ y =   - 2 =

∴ The solutions of the system of equations are (1 , -1) and ( ,   )

2 & 7

step-by-step explanation:

he climbs 300 ft/hr at a constant rate. the peak is at 1,500 ft.

when going up, he reaches 600 ft in 2 hours. remember, that he is going in a constant rate. divide 600 with 300:

600/300 = 2

assuming that he takes the same route back (meaning that it's a 1500 ft route back, you can solve.

note also that you are solving when he gets back to 600 ft after he reaches the peak.

first, find the amount of hours it takes to get up the peak. divide the total amount (1500), with the ft/her (300) to get the amount of hours (x):

1500/300 = x

x = 5

it takes jamie 5 hours to get up. now, he is returning down, and reaches 600 (his current destination). remember that he climbs at a constant 300 ft/hr. divide 600 with 300:

600/300 = x

x = 2

now add the two numbers together.

x = 5 + 2 = 7

jamie takes 7 hours to go up the mountain and reach his current position when descending.

(total amount/constant rate) = (time).

remember that it is a constant rate, so in total, when he gets back down the mountain, it will take the same amount of time as when he goes up. the total amount for the round trip is: 5 + 5 = 10.

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in geometry, parallel lines are lines in a plane which do not meet; that is, two lines in a plane that do not intersect or touch each other at any point are said to be parallel. by extension, a line and a plane, or two planes, in three-dimensional euclidean space that do not share a point are said to be parallel.