Question

1/3x-1/12y=4 6x+5y=150

Answer 1

1/3х-1/12у=34 (переноси 4 в левую часть с противоположным знаком) 1/3x-1/12y-4=0 (умножаем обе части уравнения на 12) 12*1/3x-12*1/12y-12*4=12*0 (сокращаемся числа) 4x-у-48-0 6х+5у=150(переносим 150 в левую часть с противоположным знаком) 6x+5y-150=0

Answer 2

To solve the system of equations:

1. $\frac{1}{3}x - \frac{1}{12}y = 4$
2. $6x + 5y = 150$

We can use either the substitution method or the elimination method. Let's use the elimination method in this case.

First, let's manipulate the first equation to get rid of the fractions. Multiply the entire equation by $12$ to clear the fractions:

$12 \left( \frac{1}{3}x - \frac{1}{12}y \right) = 12 \cdot 4$

Simplify:

$4x - y = 48$

Now we have the following system of equations:

1. $4x - y = 48$
2. $6x + 5y = 150$

Let's solve for $y$ in the first equation:

$y = 4x - 48$

Now substitute this expression for $y$ into the second equation:

$6x + 5(4x - 48) = 150$

Simplify:

$6x + 20x - 240 = 150$

Combine like terms:

$26x - 240 = 150$

Add $240$ to both sides:

$26x = 390$

Now, divide by $26$:

$x = 15$

Now that we have the value of $x$, substitute it back into the expression for $y$:

$y = 4x - 48 = 4 \cdot 15 - 48 = 60 - 48 = 12$

So, the solution to the system of equations is $x = 15$ and $y = 12$.