Answer to Question #222302 in Linear Algebra for Rathia

Question

3x-6y=10 and 9x+15y=-14

Answer 1

We should determine such values (x,y) that satisfy both equations:

$\begin{cases} 3x-6y=10, \\ 9x+15y=-14 \end{cases}$

Let us multiply the first equation by 3 and subtract the second equation from the first:

$\begin{cases} 9x-18y=30, \\ 9x+15y=-14 \end{cases}$ , $-33y = 44 \Rightarrow y = -\dfrac43\,.$

Next, we substitute the value of y into the first equation and obtain the value of x:

$x = \dfrac19(30 + 18y) = \dfrac19(30- 24) = \dfrac23.$

Therefore, $(x,y) = \left( \dfrac23, -\dfrac43\right).$