CHOOSE ONE system of equations, A, B, or C to use for the following questions:

A) Linear Equation: y = -x + 1
Parabolic Equation: y = x2 + x - 2

B) Linear Equation: y = 2x + 1
Parabolic Equation: y = x2 - 5x + 7

C) Linear Equation: y = -2x + 2
Parabolic Equation: y = -x2 + 2x + 7

Show all work to solve your system of equations algebraically.

I chose B

Task 1: Part 2

Graph your system of equations and show the solution graphically to verify your solution.

hello from mrbilldoesmath!

answer:   (7x + 6y) ( 49x^2 - 42xy + 36y^2)

discussion:

in general, the factorization of a^3 + b^3 is

a^3 + b^ 3 = (a + b) ( a^2 - ab + b^2)

in our case note that 343 = 7^3 and 216 = 6^3 so the equation becomes:

343x^3 + 216y^3 = (7x)^3 + (6y)^3

if you think of a (above) as 7x and b as 6y the factorization becomes

343x^3 + 216y^3 =

((7x + 6y) (   (7x)^2 - 7x*6y + (6y)^2)   =

(7x + 6y) ( 49x^2 - 42xy + 36y^2)

you,

mrb

(a + b) (a^2 - a b + b^2)

it goes right