Question

Solve the following system of liner equations:

Answer 1

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

Answer 2

Answer:

The solution of this system of equations : (-3.08,-2.84)

Step-by-step explanation:

Given : $6x-3y+10=0\\\\2x+y+9=0$

To Solve : system of liner equations

Solution :

We are given the equations :

6x-3y+10=0 -----(a)

2x+y+9=0    -----(b)

Now, solve these equatons using substitution method

Substitute the value of (y) from b in (a)

⇒6x-3(-9-2x)+10=0

⇒6x+27+6x)+10=0

⇒12x+27+10=0

⇒12x+37=0

⇒$x = \frac{-37}{12}$

⇒$x = -3.08$

Now to find value of y

put this value of x in equation (b)

⇒2(-3.08) + y + 9 = 0

⇒-6.16+ y + 9 = 0

⇒2.84+y=0

⇒y = -2.84

Thus the solution of this system of equations : (-3.08,-2.84)