Question

Реши систему уравнений способом алгебраического сложения. a−4t=5 3a−7t=39 срочнооо!!!пожалуйстаа!!)))

Answer 1

{a-4t=5
$\left \{ {{a-4t=5} \atop {3a-7t=39}} \right. ==\ \textgreater \ \left \{ {{a=5+4t} \atop {3a-7t=39}} \right. \\ 3(5+4t)-7t=39 \\ 15+12t-7t=39 \\ 5t=24 \\ t= \frac{24}{5} =4\frac{4}{5} \\ \\ a=5+4t \\ a=5+4* \frac{24}{5}=5+ \frac{96}{5}= \frac{25+96}{5}= \frac{121}{5} =24 \frac{1}{5} \\ \\ a=121/5 \\ t=24/5$

Answer 2

Solving the System of Equations using Algebraic Addition

To solve the system of equations using the method of algebraic addition, we will eliminate one variable by adding the equations together. Let's solve the given system of equations:

Equation 1: a - 4t = 5 Equation 2: 3a - 7t = 39 To eliminate the variable 'a', we can multiply Equation 1 by 3 and Equation 2 by 1, and then add the resulting equations together:

3(a - 4t) = 3(5)   =>   3a - 12t = 15
1(3a - 7t) = 1(39)   =>   3a - 7t = 39

Adding the two equations together, we get:

(3a - 12t) + (3a - 7t) = 15 + 39
6a - 19t = 54

So, the new equation we obtained is 6a - 19t = 54.

Now, we have a new equation with only one variable, 't'. We can solve for 't' using this equation.

Next, we can substitute the value of 't' back into one of the original equations to solve for 'a'. Let's use Equation 1:

a - 4t = 5
a - 4(3) = 5   (substituting the value of 't' as 3)
a - 12 = 5
a = 5 + 12
a = 17

Therefore, the solution to the given system of equations is a = 17 and t = 3.

Please let me know if you need any further assistance!