Solve the following system of liner equations:

6x - 3y + 10 = 0

2x + y + 9 = 0

First we get the value of y in terms of x

We have 2x + y + 9 = 0

We transpose 2x and 9 to the other side so we could get the value of y being:

y = - 2x - 9

Now that we have the value of y we can substitute it to the first equation

6x - 3y + 10 = 0

6x - 3 (-2x - 9) + 10 = 0

Simplifying the inside of the parentheses we would have

6x - (3) (-2x) - (3) (-9) + 10 = 0

6x + 6x + 27 + 10 = 0

Combining similar terms we would get

12x + 37 = 0

We transpose 37 to the other side for easier simplification

12x = - 37

We divide both sides by 12 to get the value of x

12x/12 = - 37/12

Since 12/12 is equal to 1 our value of x would be

x = - 37/12

Or simply x = - 3.0833

Now that we know the value of x we can use it to obtain the value of y

y = - 2x - 9

y = - 2 (-37/12) - 9

y = 37/6 - 9

y = - 17/6

Or in decimal y = - 2.8333

Final values of x and y would be

x = - 3.0833

y = - 2.8333