Q. 30

Solve each system of equations. If the system has no solution, say that it is inconsistent.

$\{\begin{matrix} 3 x - y = 7 \\ 9 x - 3 y = 21 \end{matrix}$

Verified

Answer

The given system of equations has infinite number of solutions.

1Step 1. Given information.

The given equations are:

$\begin{array}{rcl} 3 x - y & = & 7 \\ 9 x - 3 y & = & 21 \end{array}$

2Step 2. Determine one variable in terms of another variable.

The first equation can be written as:

$\begin{array}{rcl} 3 x - y & = & 7 \\ - y & = & 7 - 3 x \\ y & = & - (7 - 3 x) \\ y & = & 3 x - 7 \end{array}$

3Step 3. Determine the value of one variable.

Substitute the above value in the second equation.

$\begin{array}{rcl} 9 x - 3 (3 x - 7) & = & 21 \\ 9 x - 9 x + 21 & = & 21 \\ 21 & = & 21 \end{array}$

This statement is true for all real values. So, the given system of equations has infinite number of solutions.