Question #222302
3x-6y=10 and 9x+15y=-14
1
Expert's answer
2021-08-02T13:54:13-0400

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

{3x6y=10,9x+15y=14\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:

{9x18y=30,9x+15y=14\begin{cases} 9x-18y=30, \\ 9x+15y=-14 \end{cases} , 33y=44y=43.-33y = 44 \Rightarrow y = -\dfrac43\,.

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

x=19(30+18y)=19(3024)=23.x = \dfrac19(30 + 18y) = \dfrac19(30- 24) = \dfrac23.

Therefore, (x,y)=(23,43).(x,y) = \left( \dfrac23, -\dfrac43\right).


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