Question

1. ( 2x + 4y = 6 )
2. ( 5x - 3y + 5 = 2y - 5 )

find the least common multiple (lcm) of the following:

1. 18, 35, and 40
2. ( 2, c^2, ) and ( c^3 )

add:

Explanation:

Problem 13:

Step1: Isolate the x-term

$2x = 6 - 4y$

Step2: Solve for x

$x = \frac{6 - 4y}{2} = 3 - 2y$

Step1: Group like terms

$5x - 2y = -5 - 3 + 5$

Step2: Simplify constants

$5x - 2y = -3$

Step1: Prime factorize each number

$18 = 2 \times 3^2$, $35 = 5 \times 7$, $40 = 2^3 \times 5$

Step2: Take highest powers of primes

$\text{LCM} = 2^3 \times 3^2 \times 5 \times 7$

Step3: Calculate the product

$\text{LCM} = 8 \times 9 \times 5 \times 7 = 2520$

Answer:

$x = 3 - 2y$ (or rearranged as $2x + 4y = 6$ simplified to $x + 2y = 3$)

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Problem 14: