Question

What is the solution to the following system of equations? (1 point) x − 3y = 6 2x + 2y = 4

Answer 1

(3, - 1 )

Explanation:

x - 3y = 6 ( add 3y to both sides )

x = 3y + 6 → (1)

2x + 2y = 4 → (2)

substitute x = 3y + 6 into (2)

2(3y + 6) + 2y = 4

6y + 12 + 2y = 4

8y + 12 = 4 ( subtract 12 from both sides )

8y = - 8 ( divide both sides by 8 )

y = - 1

substitute y = - 1 into (1)

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

solution is (3, - 1 )

Answer 2

x = 3

y = -1

Explanation:

Solving system of equations:

Method: substitution

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

x = 6 + 3y -------------(II)

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

Substitute x = 6 +3y in equation (II),

2*(6+3y) + 2y = 4

Use distributive property to open the parenthesis,

2*6 + 2*3y + 2y = 4

12 + 6y + 2y = 4

Combine like terms.

12 + 8y = 4

Subtract 12 from both sides,

8y = 4 - 12

8y = -8

Divide both sides by 8,

y = -8÷ 8

`\boxed{\bf y = (-1)}\\`

Substitute y = -1 in equation (II) and find the value of x.

x = 6 + 3*(-1)

= 6 - 3

`\sf \boxed{\bf x = 3}`