Question

algebra 1 - chapter 5 - homework packet
5-80. write an equation or system of equations to solve the problem below.
apollo and zeus are both on diets. apollo currently weighs 105 kg and is gaining 2 kg per month. zeus currently weighs 130 kg and is losing 3 kg per month. in how many months will they weigh the same?
5-81. solve each system.
$6x - 2y = 10$
$3x - 2 = y$
$3x - 9y = 3$
$2x = 16 - y$

Explanation:

Problem 5-80:

Step1: Define variables and equations

Let $x$ = number of months, $W_A$ = Apollo's weight, $W_Z$ = Zeus's weight.
$W_A = 105 + 2x$
$W_Z = 130 - 3x$
Set $W_A = W_Z$: $105 + 2x = 130 - 3x$

Step2: Isolate x terms

$2x + 3x = 130 - 105$
$5x = 25$

Step3: Solve for x

$x = \frac{25}{5}$
$x = 5$

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Problem 5-81 (Left System):

Step1: Substitute $y=3x-2$

Substitute into $6x-2y=10$:
$6x - 2(3x-2) = 10$

Step2: Simplify the equation

$6x - 6x + 4 = 10$
$4 = 10$

Step3: Analyze the result

False statement, so no solution.

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Problem 5-81 (Right System):

Step1: Rearrange second equation

$2x = 16 - y \implies y = 16 - 2x$

Step2: Substitute into first equation

Substitute $y=16-2x$ into $3x-9y=3$:
$3x - 9(16-2x) = 3$

Step3: Expand and simplify

$3x - 144 + 18x = 3$
$21x = 147$

Step4: Solve for x

$x = \frac{147}{21}$
$x = 7$

Step5: Solve for y

$y = 16 - 2(7)$
$y = 16 - 14 = 2$

Answer:

5-80: 5 months
5-81 (Left System): No solution
5-81 (Right System): $x=7$, $y=2$ (or the ordered pair $(7, 2)$)