Question

1/4x+1/2y = 5/3a-2/9b= a/6m+b/8n= x/12a-y/18b=

Answer 1

Ответ:

1) y+2x\4xy.

2) 13\9ab.

3) 4an + 3bm\24mn.

4) 3bx - 2ay\36ab.

Объяснение:

1) Домножаем 1\4x на y, а 1\2y на 2x и получаем знаменатель 4xy.

=>  y+2x\4xy.

2) Домножаем 5\3a на 3b, а 2\9b на a и получаем знаменатель 9ab.

=> 15-2\9ab = 13\9ab.

3) Домножаем a\6m на 4n, а b\8n на 3m и получаем знаменатель 24mn.

=> 4an + 3bm\24mn.

4) Домножаем x\12a на 3b, а y\18b на 2a и получаем знаменатель 36ab

=> 3bx - 2ay\36ab.

Answer 2

It appears that you have a system of linear equations with multiple variables. To solve this system, we can use the method of substitution or elimination. Let's solve this step by step.

The given equations are:

1. $\frac{1}{4}x + \frac{1}{2}y = \frac{5}{3}a - \frac{2}{9}b$
2. $\frac{5}{3}a - \frac{2}{9}b = \frac{a}{6}m + \frac{b}{8}n$
3. $\frac{a}{6}m + \frac{b}{8}n = \frac{x}{12}a - \frac{y}{18}b$

Let's solve for the variables step by step:

Step 1: Solve equations 1 and 2 for $a$ and $b$

From equation 2: $\frac{5}{3}a - \frac{2}{9}b = \frac{a}{6}m + \frac{b}{8}n$

Cross-multiply to eliminate fractions: $40a - 12b = 3am + 4bn$

Rearrange to solve for $b$: $12b + 4bn = 40a - 3am$ $b(12 + 4n) = a(40 - 3m)$ $b = \frac{a(40 - 3m)}{12 + 4n}$

Now substitute $b$ in equation 1: $\frac{1}{4}x + \frac{1}{2}y = \frac{5}{3}a - \frac{2}{9}b$ $\frac{1}{4}x + \frac{1}{2}y = \frac{5}{3}a - \frac{2}{9} \cdot \frac{a(40 - 3m)}{12 + 4n}$

Simplify: $\frac{1}{4}x + \frac{1}{2}y = \frac{5}{3}a - \frac{8a(40 - 3m)}{9(12 + 4n)}$

Step 2: Solve equations 3 and the simplified equation for $a$ and $x$

From equation 3: $\frac{a}{6}m + \frac{b}{8}n = \frac{x}{12}a - \frac{y}{18}b$

Substitute the expression for $b$ from step 1: $\frac{a}{6}m + \frac{a(40 - 3m)}{8(12 + 4n)}n = \frac{x}{12}a - \frac{y}{18} \cdot \frac{a(40 - 3m)}{12 + 4n}$

Now you have an equation relating $a$ and $x$. You can solve for $x$ in terms of