Question

How many solutions does the following equation have?

7(y+3)=5y+8
A. No Solution
B. Exactly One Solution
C. Infinitely many solutions

Answer 1

B. Exactly one solution

7y +21 = 5y +8
7y +13=5y
13=-2y
-6.5=y

Answer 2

B. Exactly One Solution

Explanation:

Given:

`7(y+3)=5y+8`

Expand the brackets:

`\implies 7y + 21 = 5y + 8`

Subtract 21 from both sides:

`\implies 7y + 21-21 = 5y + 8-21`

`\implies 7y=5y-13`

Subtract 5y from both sides:

`\implies 7y-5y=5y-13-5y`

`\implies 2y=-13`

Divide both sides by 2:

`\implies (2y)/(2)=(-13)/(2)`

`\implies y=-(13)/(2)`

Therefore, the equation has exactly one solution.