Problem

Solve the system by the method of your choice. \[ \left\{\begin{array}{l} y=3 x-2 \\ 9 x-6=3 y \end{array}\right. \]

Solution

Step 1 :First, we can substitute the first equation into the second equation. From \(9x - 6 = 3(3x - 2)\), we get \(9x - 6 = 9x - 6\).

Step 2 :This equation is always true, regardless of the value of \(x\), which means that there are infinitely many solutions to this system of equations.

Step 3 :However, since \(y = 3x - 2\), we can express the solutions as ordered pairs \((x, y)\) where \(y = 3x - 2\).

Step 4 :Thus, the solution to the system of equations is all ordered pairs \((x, 3x - 2)\) where \(x\) is a real number.

From Solvely APP
Source: https://solvelyapp.com/problems/19114/

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