Question

by elimination.

1. \\(\

$$\begin{cases}10x + 3y = 27 \\\\ 7x - 14y = 35\\end{cases}$$

\\)

Explanation:

Step1: Simplify the second equation

Divide the second equation \(7x - 14y = 35\) by 7, we get \(x - 2y = 5\), then express \(x\) as \(x = 2y + 5\).

Step2: Substitute \(x\) into the first equation

Substitute \(x = 2y + 5\) into \(10x + 3y = 27\), we have \(10(2y + 5) + 3y = 27\).
Expand the left side: \(20y + 50 + 3y = 27\).
Combine like terms: \(23y + 50 = 27\).
Subtract 50 from both sides: \(23y = 27 - 50 = -23\).
Divide both sides by 23: \(y = -1\).

Step3: Find the value of \(x\)

Substitute \(y = -1\) into \(x = 2y + 5\), we get \(x = 2\times(-1) + 5 = 3\).

Answer:

The solution of the system of equations is \(x = 3\), \(y = -1\)