Question

x+3y=4; 2x-6y=4.find the value of x and y.

Answer 1

Answer to Question#39552 - Math - Algebra

Question: $\begin{cases} x + 3y = 4; \\ 2x - 6y = 4. \end{cases}$

Find the value of $x$ and $y$.

Solution. Let us express $x$ as a function of $y$ from the first equation:

$$x = 4 - 3y$$

We can now substitute this into the second equation:

$$2(4 - 3y) - 6y = 4$$

And find $y$:

$$\begin{array}{l} 8 - 6y - 6y = 4 \\ -12y = -4 \\ y = \frac{1}{3} \end{array}$$

This also gives us the value of $x$:

$$x = 4 - 3 \cdot \frac{1}{3} = 4 - 1 = 3.$$

Thus, the solution of the given system is the pair of values $x = 3, y = \frac{1}{3}$.

Answer. $x = 3, y = \frac{1}{3}$.