How many solutions does this equation have? 3y − 7 = 2y Choices: (A)no solution (B)one solution (C)infinitely many solutions

Isolate variable y: Isolate the variable y on one side of the equation. 3y - 7 = 2y Subtract 2y from both sides to get: 3y - 2y - 7 = 2y - 2ySimplify equation: Simplify both sides of the equation. 3y - 2y - 7 = 0 y - 7 = 0Add 7 to solve: Add 7 to both sides to solve for y. y - 7 + 7 = 0 + 7 y = 7Check solution: Check if the solution y = 7 satisfies the original equation. 3(7) - 7 = 2(7) 21 - 7 = 14 14 = 14 This is true, so y = 7 is a solution.

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How many solutions does this equation have? $\newline$ $3y - 7 = 2y$ $\newline$ Choices: $\newline$ (A)no solution $\newline$ (B)one solution $\newline$ (C)infinitely many solutions

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Math Problems

Algebra 1

Find the number of solutions to a linear equation

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Q. How many solutions does this equation have?

\newline

3y - 7 = 2y

\newline

Choices:

\newline

(A)no solution

\newline

(B)one solution

\newline

(C)infinitely many solutions

Isolate variable y: Isolate the variable y on one side of the equation. $\newline$ $3y - 7 = 2y$ $\newline$ Subtract $2y$ from both sides to get: $\newline$ $3y - 2y - 7 = 2y - 2y$
Simplify equation: Simplify both sides of the equation. $\newline$ $3y - 2y - 7 = 0$ $\newline$ $y - 7 = 0$
Add $7$ to solve: Add $7$ to both sides to solve for $y$ . $y - 7 + 7 = 0 + 7$ $y = 7$
Check solution: Check if the solution $y = 7$ satisfies the original equation. $3(7) - 7 = 2(7)$ $21 - 7 = 14$ $14 = 14$ This is true, so $y = 7$ is a solution.