Question

PLEASE HELPP

What is the solution to the following system of equations?

x − 3y = 6
2x + 2y = 4

(-1, 3)
(3, -1)
(1, -3)
(-3, 1)

Answer 1

A N S W E R :

• x - 3y = 6 ......[Equation (i) ]
• 2x + 2y = 4 ......[Equation (ii)]

⚽ From Equation (i) we get :

• x = 6 + 3y......[Equation (iii)]

⚽ Now, Substitute the equation (iii) in equation (ii) we get :

→ 2(6 + 3y) + 2y = 4

→ 12 + 6y + 2y = 4

→ 8y = 4 - 12

→ 8y = -8

→ y = -8 ÷ 8

→ y = -1

⚽ Now Substituting value of y = -1 in equation (iii) we get :

→ x = 6 + 3y

→ x = 6 + 3(-1)

→ x = 6 + (-3)

→ x = 6 - 3

→ x = 3

• Hence,the value of x = 3 and value of y = -1.

Answer 2

The solution to the system of equations be:

`x=3,\:y=-1`

Hece, option B is correct.

Explanation:

Given the system of equations

`\begin{bmatrix}x-3y=6\\ 2x+2y=4\end{bmatrix}`

Multiply x − 3y = 6 by 2: 2x-6y=12

`\begin{bmatrix}2x-6y=12\\ 2x+2y=4\end{bmatrix}`

so

`2x+2y=4`

`-`

`\underline{2x-6y=12}`

`8y=-8`

so the system of equations becomes

`\begin{bmatrix}2x-6y=12\\ 8y=-8\end{bmatrix}`

Solve 8y = -8 for y

`8y=-8`

Divide both sides by 8

`(8y)/(8)=(-8)/(8)`

`y=-1`

`\mathrm{For\:}2x-6y=12\mathrm{\:plug\:in\:}y=-1`

`2x-6\left(-1\right)=12`

`2x+6=12`

subtract 6 from both sides

`2x+6-6=12-6`

`2x=6`

Divide both sides by 2

`(2x)/(2)=(6)/(2)`

`x=3`

Therefore, the solution to the system of equations be:

`x=3,\:y=-1`

Hence, option B is correct.