Solving a Two-Step Matrix Equation
Solve the equation:

Step-by-step explanation:

Solve the following equation:

-In order to solve a pair of equations by using substitution, you first need to solve one of the equations for one of variables and then you would substitute the result for that variable in the other equation:

-First equation:

-Second equation:

-Choose one of the two following equations, which I choose the first one, then you solve for by isolating

-Subtract to both sides:

-Subtract to both sides:

-Divide both sides by :

-Multiply by :

-Substitute for in the second equation, which is :

Multiply by :

-Combine like terms:

-Subtract to both sides:

-Multiply both sides by :

-After you have the value of , substitute for onto this equation, which is :

-Multiply and :

-Since both and have the same denominator, then add the numerators together. Also, after you have added both numerators together, reduce the fraction to the lowest term:

this is the formula: v = the value of investment at the end of the time period

p = the principal amount (the initial amount invested)

r = the annual interest rate

n = the annual frequency of compounding (how many times a year interest is added)

t = the number of years the money is invested

^ means raise to the power of

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)