Question

Solve the system of equations:10x+y=-180=5x+3y+4

Answer 1

First clear one variable of any equation, I will choose the x from the first:

$10x+y=-18$$10x=-18-y$$x=\frac{-18-y}{10}$

Now replace in the second:

$0=5x+3y+4$$0=5(\frac{-18-y}{10})+3y+4$$5\left(\frac{-18-y}{10}\right)+3y+4=0$$5\cdot \frac{-18-y}{10}+3y+4-4=0-4$$5\cdot \frac{-18-y}{10}+3y=-4$$-9+\frac{5y}{2}=-4$$-9\cdot \:2+\frac{5y}{2}\cdot \:2=-4\cdot \:2$$-18+5y=-8$$-18+5y+18=-8+18$$5y=10$$y=2$

Now replace first the y:

$x=\frac{-18-y}{10}$$x=\frac{-18-2}{10}$$x=\frac{-20}{10}$$x=-2$

x=-2

y=2