Question

Solve the system of equations below algebraically

5y + 3x = -10
\[-\frac{ 5 }{ 3 }y = x - \frac{ 4 }{ 3 }\]

Answer 1

First I'd start off by multiplying both sides of equation two by the LCD 3 to go from

\[\Large -\frac{ 5 }{ 3 }y = x - \frac{ 4 }{ 3 }\]

to

\[\Large -5y = 3x - 3\]

Answer 2

Then subtract 3x from both sides to get

\[\Large -5y = 3x - 3\]

\[\Large -5y - 3x = - 3\]

\[\Large -3x - 5y = - 3\]

Answer 3

So you now have the system

5y + 3x = -10
-3x - 5y = -3

which is really the same thing as this system

3x + 5y = -10
-3x - 5y = -3

I'll let you finish up