How many solutions does the following equation have? 13(y+3)=13 y+39 Choose 1 answer: (A) No solutions (B) Exactly one solution (C) Infinitely many solutions

Distribute 13 to both terms: Distribute 13 to both terms inside the parentheses on the left side of the equation. 13(y+3) = 13y + 39 13*y + 13*3 = 13y + 39 13y + 39 = 13y + 39Observe identical sides: Observe that both sides of the equation are identical. 13y + 39 = 13y + 39 This equation is true for all values of y.Infinite solutions: Since the equation is true for all values of y, the equation has infinitely many solutions.

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How many solutions does the following equation have?

13(y+3)=13 y+39
Choose 1 answer:
(A) No solutions
(B) Exactly one solution
(C) Infinitely many solutions

How many solutions does the following equation have? $\newline$ $13(y+3)=13y+39$ $\newline$ Choose $1$ answer: $\newline$ (A) No solutions $\newline$ (B) Exactly one solution $\newline$ (C) Infinitely many solutions

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Math Problems

Algebra 1

Find the number of solutions to a linear equation

Full solution

Q. How many solutions does the following equation have?

\newline

13(y+3)=13y+39

\newline

Choose

1

answer:

\newline

(A) No solutions

\newline

(B) Exactly one solution

\newline

Distribute $13$ to both terms: Distribute $13$ to both terms inside the parentheses on the left side of the equation. $\newline$ $13(y+3) = 13y + 39$ $\newline$ $13y + 13 \cdot 3 = 13y + 39$ $\newline$ $13y + 39 = 13y + 39$
Observe identical sides: Observe that both sides of the equation are identical. $\newline$ $13y + 39 = 13y + 39$ $\newline$ This equation is true for all values of $y$ .
Infinite solutions: Since the equation is true for all values of $y$ , the equation has infinitely many solutions.