\( 6 ( a , b ) = ( 2 - a , 2 b - 3 ) \)

The given equation is \(6(a, b) = (2 - a, 2b - 3)\). To solve this equation, we need to find the values of \(a\) and \(b\) that satisfy the equation. Let's start by expanding the left side of the equation: \(6(a, b) = (6a, 6b)\) Now, we can equate the corresponding components of the two sides of the equation: \(6a = 2 - a\) (for the x-component) \(6b = 2b - 3\) (for the y-component) Solving these two equations will give us the values of \(a\) and \(b\). Solve the system of equations by following steps: - step0: Solution: \(\left\{ \begin{array}{l}6a=2-a\\6b=2b-3\end{array}\right.\) - step1: Calculate: \(\left\{ \begin{array}{l}a=\frac{2}{7}\\b=-\frac{3}{4}\end{array}\right.\) - step2: Check the solution: \(\left\{ \begin{array}{l}a=\frac{2}{7}\\b=-\frac{3}{4}\end{array}\right.\) - step3: Rewrite: \(\left(a,b\right) = \left(\frac{2}{7},-\frac{3}{4}\right)\) The solution to the system of equations is \(a = \frac{2}{7}\) and \(b = -\frac{3}{4}\). Therefore, the values of \(a\) and \(b\) that satisfy the equation \(6(a, b) = (2 - a, 2b - 3)\) are \(a = \frac{2}{7}\) and \(b = -\frac{3}{4}\).