Question 16.1.2: Use (16.1.4) to find the solutions of 2x1 + 4x2 = 7 2x1 − 2x......
Use (16.1.4) to find the solutions of
2x_{1}+4x_{2}=~~~72x_{1}-2x_{2}=-2
x_{1}=\frac{1}{\left|A\right| } \left | \begin{matrix} b_{1} & a_{12} \\ b_{2} & a_{22} \end{matrix} \right | and x_{2}=\frac{1}{\left|A\right| } \left | \begin{matrix} a_{11} & b_{1} \\ a_{21} & b_{2} \end{matrix} \right | (16.1.4)
Step-by-Step
x_{1}=\frac{\left | \begin{matrix} 7 & 4 \\ -2 & -2 \end{matrix} \right | }{\left | \begin{matrix} 2 & 4 \\ 2 & -2 \end{matrix} \right | } =\frac{-6}{-12}=\frac{1}{2} and x_{2}=\frac{\left | \begin{matrix} 2 & 7 \\ 2 & -2 \end{matrix} \right | }{\left | \begin{matrix} 2 & 4 \\ 2 & -2 \end{matrix} \right | } =\frac{-18}{-12}=\frac{3}{2}
Check by substitution that x_{1} = 1/2, x_{2} = 3/2 really is a solution.
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