Question

What is the value of y in the solution to the system of equations?x + y = 12x – 3y = –30

Answer 1

Answer:

There are three possibilities for the given question,

Case 1 : if question is,

x + y = 12 -----(1) ; x - 3y = - 30 -----(2),

Subtraction equation (1) and Equation (2),

We get,

4y = 42

$\implies y = \frac{42}{4}=\frac{21}{2}$

Case 2 :

If the equations are,

x + y = 1 ----(1);  2x - 3y = -30-----(2),

Equation (2) - 2 × Equation (1),

We get,

-5y = -32

$\implies y=\frac{32}{5}$

Case 3 :

if the equations are,

x + y = 12x - 3y = - 30

⇒ x + y = - 30 ------(1)

And, 12x - 3y = - 30 ------(2)

Equation (2) - 12 × Equation (1),

We get,

-3y - 12y = - 30 + 360

⇒ - 15 y = 330

Dividing both sides by - 15,

⇒ y = -22

Answer 2

X+y=-30
12x-3y=-30
Multiply equation 1 by 12
12x+12y=-360
12x-3y=-30
-------------
15y=-330
x=-22