Question

What is the solution to the following system of equations?

X – 3y = 6
2x + 2y = 4

A.y=-1

B.x=3

C.y=3

D.x=-1​

Answer 1

x = 3, y = -1 ⇒ AB

Explanation:

`\left\{\begin{array}{ccc}x-3y=6&\text{multiply both sides by (-2)}\\2x+2y=4\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}-2x+6y=-12\\2x+2y=4\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad8y=-8\qquad\text{divide both sides by 8}\\.\qquad\qquad y=-1\\\\\text{Put the value of y to the first equation:}\\\\x-3(-1)=6\\x+3=6\qquad\text{subtract 3 from both sides}\\x=3`

Answer 2

Answer: y = -1 and x = 3

Explanation:

x - 3y = 6 --------(1)

2x + 2y = 4 -------(2)

we multiply (1) by 2

2x - 6y = 12 --------(3)

(3) - (1)

-8y = 8

y = -1

Putting y = -1 into equation (1)

x - 3 (-1) = 6

x + 3 =6

collect the like term

x = 6 - 3

x = 3

Therefore x= 3 and y = -1