Question

Solve using Gaussian eliminationX+2y=7. And. Y=3x+2

Answer 1

$\begin{cases}x+2y=7_{\text{ }}(1){} \\ y=3x+2_{\text{ }}(2){}\end{cases}$

Let's rewrite the system as:

$\begin{cases}x+2y=7_{\text{ }}{(1)} \\ 3x-y={-2_{\text{ }}}(2)\end{cases}$

Using elimination:

$\begin{gathered} (1)+2(2) \\ x+6x+2y-2y=7-4 \\ 7x=3 \\ x=\frac{3}{7} \end{gathered}$

Replace x into (2):

$\begin{gathered} y=3(\frac{3}{7})+2 \\ y=\frac{23}{7} \end{gathered}$