How many solutions does the following equation have? -6y+13+9y=8y-3 Choose 1 answer: (A) No solutions (B) Exactly one solution (C) Infinitely many solutions

Combine like terms: Combine like terms on the left side of the equation. -6y + 13 + 9y = 3y + 13Rewrite equation: Rewrite the equation with the simplified left side. 3y + 13 = 8y - 3Subtract y terms: Subtract 3y from both sides to get all the y terms on one side. 3y + 13 - 3y = 8y - 3 - 3y 0 + 13 = 5y - 3 13 = 5y - 3Add to isolate y: Add 3 to both sides to isolate the y term. 13 + 3 = 5y - 3 + 3 16 = 5yDivide to solve for y: Divide both sides by 5 to solve for y. 16 / 5 = 5y / 5 y = 16 / 5One solution: Since we found a specific value for y, the equation has exactly one solution.

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How many solutions does the following equation have?

-6y+13+9y=8y-3
Choose 1 answer:
(A) No solutions
(B) Exactly one solution
(C) Infinitely many solutions

How many solutions does the following equation have? $\newline$ $-6y+13+9y=8y-3$ $\newline$ 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

-6y+13+9y=8y-3

\newline

Choose

1

answer:

\newline

(A) No solutions

\newline

(B) Exactly one solution

\newline

Combine like terms: Combine like terms on the left side of the equation. $\newline$ $-6y + 13 + 9y$ $\newline$ $= 3y + 13$
Rewrite equation: Rewrite the equation with the simplified left side. $\newline$ $3y + 13 = 8y - 3$
Subtract y terms: Subtract $3y$ from both sides to get all the y terms on one side. $\newline$ $3y + 13 - 3y = 8y - 3 - 3y$ $\newline$ $0 + 13 = 5y - 3$ $\newline$ $13 = 5y - 3$
Add to isolate y: Add $3$ to both sides to isolate the $y$ term. $\newline$ $13 + 3 = 5y - 3 + 3$ $\newline$ $16 = 5y$
Divide to solve for y: Divide both sides by $5$ to solve for y. $\frac{16}{5} = \frac{5y}{5}$ $y = \frac{16}{5}$
One solution: Since we found a specific value for $y$ , the equation has exactly one solution.