Question

Use the graphing calculator to locate the solutions of this system of equations:

Answer 1

Hello,

y=(x-2)²-15
y=5x-1

==> 5x-1=x²-4x+4-15
==> x²-9x-10=0
Δ=9²+4*10=11²
x=(9+11)/2 or x=(9-11)/2
==>(x=10 and y=5*10-1=49) or (x=-1 and y=5*(-1)-1=-6)

1) A (-1,-6)
2) C (10,49)

Answer 2

Answer:

Option A (-1, -6)

Option C (10, 49)

Step-by-step explanation:

Two equations are given as y = (x - 2)² - 15 ----------(1)

and -5x + y = -1

y = -1 + 5x ------(2)

We put the value of y from equation 1 in equation 2.

(x -2)² - 15 = 5x - 1

x² + 4 - 4x - 15 = 5x - 1

x²- 4x - 11 = 5x - 1

x² - 4x - 11 - 5x + 1 = 0

x² - 9x - 10 = 0

x² - 10x + x - 10 = 0

x(x - 10) + 1(x - 10) = 0

(x + 1)(x - 10) = 0

x = -1 , 10

Now we put the value of x in equation 2

y = 5(-1) - 1

y = -5 -1 = -6

For x = 10

y = 5×10 - 1 = 50 - 1 = 49

So solutions are (-1, -6) and (10, 49)

First solution is Option A. (-1, -6) and second solution is Option C.(10, 49)