Question

1,7x+y=4,4 3,5x-0,8y=6,2

Answer 1

Пошаговое объяснение:

$\begin {cases}1.7x + y = 4.4 \: \: | \times 10\\ 3.5x - 0.8y = 6.2 \: \: | \times 10\end {cases}⇔\begin {cases}17x + 10y = 44 \: \: | \times 4 \\ 35x - 8y = 62 \: \: | \times 5 \end {cases}⇔\begin {cases}68x + 40y = 176 \\ 175x - 40y = 310\end {cases} \\ 243x = 486 \\ x = 2 \\ 34 + 10y = 44 \\ y = 1$

Answer 2

To solve this system of equations, you can use either the substitution method or the elimination method. I'll use the elimination method here.

First, let's rewrite the equations with simplified decimal coefficients:

$1.7x + y = 4.4$
$3.5x - 0.8y = 6.2$

To eliminate one of the variables, you can multiply the first equation by 0.8 (to make the coefficient of $y$ in both equations the same) and subtract the modified first equation from the second equation:

$$\begin{align*} 0.8(1.7x + y) &= 0.8(4.4) \\ 3.5x - 0.8y &= 6.2 \\ \end{align*}$$

Simplifying:

$$1.36x + 0.8y = 3.52$$

$$3.5x - 0.8y = 6.2$$

Now, add these equations to eliminate $y$:

$$(1.36x + 0.8y) + (3.5x - 0.8y) = 3.52 + 6.2$$

Solving for $x$:

$$4.86x = 9.72$$

$$x = \frac{9.72}{4.86}$$

$$x = 2$$

Now that you have the value for $x$, substitute it back into either of the original equations to solve for $y$. Using the first equation:

$$1.7x + y = 4.4$$

$$1.7(2) + y = 4.4$$

$$3.4 + y = 4.4$$

$$y = 4.4 - 3.4$$

$$y = 1$$

Therefore, the solution to the system of equations is $x = 2$ and $y = 1$.