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Solve each of the following systems of equations. Find all solutions and explain.

(a)\(\begin{align*} x+y&=-1,\\ 3x &= 4-3y. \end{align*}\)

(b)\(\begin{align*} 3x - 4y + 2&=0,\\ 10 - 10y& = 10y - 15x. \end{align*}\)

 Apr 26, 2023
 #2
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The first one: separate y in both of them to set the equations equal.

y=-1-x

y=4/3-x

Then

4/3-x=-1-x

4/3=-1

Since that is not true, there are no solutions to the first system of equations.

The second one:

3x+2=4y

3x/4+1/2=y

20y=10+15x

y=1/2+3x/4

Then

3x/4+1/2=3x/4+1/2

So, since that is true for all x, any (x,y) that matches the first equation matches the second one as well.

 May 3, 2023

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