Question

2. Given: -2x =4y +62(2y+3) =3x -5What is the solution (x,y)?I

Answer 1

this is a 2x2 system of equations.

Let:

-2x = 4y + 6 (1)

and

2(2y+3) = 3x - 5 (2)

Let's rewrite (1) as:

2x + 4y = -6 (1)

and (2) as:

3x - 4y = 11 (2)

Now, from (1)

Let's solve for x:

2x + 4y = -6

Subtract 4y from both sides:

2x + 4y - 4y = -6 - 4y

2x = -6 - 4y

Divide both sides by 2:

2x/2 = (-6 - 4y)/2

x = -3 - 2y (3)

Replacing (3) into (2)

3x - 4y = 11

3(-3 - 2y) - 4y = 11

Using distributive property:

-9 - 6y - 4y = 11

Add like terms:

-10y - 9 = 11

Add 9 to both sides:

-10y - 9 + 9 = 11 + 9

-10y = 20

Divide both sides by -10:

(-10y)/-10 = 20/-10

y = -2

Finally, replace the value of y into (3)

x = -3 - 2y

x = -3 - 2(-2)

x = -3 + 4

x = 1

Therefore the solution is :

x= 1 and y=-2

(x,y) = (1,-2)