Solve algebraically please URGENT y=5x−7 −6x−4y=−24

1 answer:

7 0

$\left\{\begin{array}{ccc}y=5x-7\\-6x-4y=-24&\text{divide both sides by (-2)}\end{array}\right\\\left\{\begin{array}{ccc}y=5x-7&(*)\\3x+2y=12&(**)\end{array}\right\\\\\text{substitute }\ (*)\ \text{to}\ (**):\\\\3x+2(5x-7)=12\qquad\text{use distributive property}\\\\3x+(2)(5x)+(2)(-7)=12\\\\3x+10x-14=12\qquad\text{add 14 to both sides}\\\\13x=26\qquad\text{divide oth sides by 13}\\\\\boxed{x=2}\\\\\text{Put the vaalue of x to}\ (*):\\\\y=5(2)-7\\\\y=10-7\\\\\boxed{y=3}\\\\Answer:\ \boxed{x=2\ and\ y=3\to(2,\ 3)}$

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Laura retired from her job recently, and she has saved about $414,731.00 over the course of her career. She plans to withdraw $2

ipn [44]

Answer:

15 months.

Step-by-step explanation:

Given:

Laura retired and saved about $414,731.00 over the course of her career.

She plans to withdraw $2,224.00 each month to pay for living expenses.

After a certain amount of time, the balance in Laura's account is $381,371.00

Question asked:

How many months have passed since Laura retired ?

Solution:

Let total number of months for which she withdrew = $x$

Total saving amount = $414,731

Unitary method:

In 1 month she withdrew = $2,224

In $x$ months she withdrew = $\$2224x$

Total withdrew amount = $\$2224x$

Balance amount after $x$ months = $381,371

Balance amount = Total saving amount - Total withdrew amount

$381371=414731-2224x\\ \\ Subtracting\ both\ sides\ by\ 414731\\ \\ 381371-414731=414731-414731-2224x\\ \\- 33360=-2224x\\ \\ Minus\ canceled\ by\ minus\\ \\ 33360=2224x\\ \\ Dividing\ both\ sides\ by\ 2224\\ \\ \frac{33360}{2224} =\frac{2224x}{2224} \\ \\ 15=x$