Question

Solve the system of equations. y = x − 5 and y = x2 − 5x + 3 A. (-4,-9) and (-2,-7) B. (4,-9) and (2,-7) C. (4,-3) and (2,-1) D. (4,-1) and (2,-3)

Answer 1

D

Explanation:

Given the 2 equations

y = x - 5 → (1)

y = x² - 5x + 3 → (2)

Substitute y = x² - 5x + 3 into (1)

x² - 5x + 3 = x - 5 ← subtract x - 5 from both sides

x² - 6x + 8 = 0 ← in standard form

(x - 2)(x - 4) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 2 = 0 ⇒ x = 2

x - 4 = 0 ⇒ x = 4

Substitute each of these values into (1) for corresponding values of y

x = 2 → y = 2 - 5 = - 3 ⇒ (2, - 3 )

x = 4 → y = 4 - 5 = - 1 ⇒ (4, - 1 )

Answer 2

Answer: (4, -1) and (2, -3) (D)

Explanation:

From equation (1)

y = x- 5 ------------------- 1

y = x² -5x + 3 ------------2

Equate the 1 and 2 together since they are the same y, if plotted on the graph it is going to be quadratic and linear .

Now solve the two together becomes

x² - 5x + 3 = x - 5

x²- 5x - x + 3 + 5 = 0

x² - 6x + 8 =0

Solve using any method

x² - 2x - 4x + 8 =0

Here I used grouping methof

x(x - 2) - 4(x - 2) = 0

(x - 2)(x - 4) = 0

x = 2 or 4.

Now to find y,

Consider equation 1 by substitute for x

y = x - 5

When x = 2, y = 2 - 5

y = -3,

When x = 4, y = 4 - 5

y = -1

The coordinate

= (2, - 3) ; ( 4, -1)

Therefore the answer is D.