Question

Solve the system of equations.
х = бу - 3
2x + 7y = 13

Answer 1

To solve the system of equations, we start with the given equations:

1. \( x = 7y - 3 \)
2. \( 2x + 7y = 13 \)

We will substitute the expression for \( x \) from the first equation into the second equation.

Substituting \( x = 7y - 3 \) into the second equation:

\[
2(7y - 3) + 7y = 13
\]

Now, distribute the 2:

\[
14y - 6 + 7y = 13
\]

Combine like terms:

\[
21y - 6 = 13
\]

Next, add 6 to both sides:

\[
21y = 19
\]

Now, divide by 21:

\[
y = \frac{19}{21}
\]

Now that we have \( y \), we can substitute this value back into the first equation to find \( x \):

\[
x = 7\left(\frac{19}{21}\right) - 3
\]

Calculating \( 7 \times \frac{19}{21} \):

\[
x = \frac{133}{21} - 3
\]

Convert \( 3 \) into a fraction:

\[
3 = \frac{63}{21}
\]

Now, perform the subtraction:

\[
x = \frac{133}{21} - \frac{63}{21} = \frac{70}{21}
\]

Now simplify \( \frac{70}{21} \):

\[
x = \frac{10}{3}
\]

So, the solution to the system of equations is:

\[
x = \frac{10}{3}, \quad y = \frac{19}{21}
\]

Therefore, the final answer is:

\[
\left( x, y \right) = \left( \frac{10}{3}, \frac{19}{21} \right)
\]