How many solutions does the following equation have? 23 y+50+27 y=50 y+50 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. 23y + 50 + 27y = (23 + 27)y + 50 = 50y + 50Compare left and right sides: Compare the simplified left side of the equation with the right side. The left side is 50y + 50, and the right side is 50y + 50. Since both sides of the equation are identical, the equation is true for every value of y.Determine number of solutions: Determine the number of solutions. Because the equation 50y + 50 = 50y + 50 is true for any value of y, the equation has infinitely many solutions.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

How many solutions does the following equation have?

23 y+50+27 y=50 y+50
Choose 1 answer:
(A) No solutions
(B) Exactly one solution
(c) Infinitely many solutions

How many solutions does the following equation have? $\newline$ $23y + 50 + 27y = 50y + 50$ $\newline$ Choose $1$ answer: $\newline$ (A) No solutions $\newline$ (B) Exactly one solution $\newline$ (C) Infinitely many solutions

View step-by-step help

Home

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

23y + 50 + 27y = 50y + 50

\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. $\newline$ $23y + 50 + 27y$ $\newline$ = $(23 + 27)y + 50$ $\newline$ = $50y + 50$
Compare left and right sides: Compare the simplified left side of the equation with the right side. $\newline$ The left side is $50y + 50$ , and the right side is $50y + 50$ . $\newline$ Since both sides of the equation are identical, the equation is true for every value of $y$ .
Determine number of solutions: Determine the number of solutions. $\newline$ Because the equation $50y + 50 = 50y + 50$ is true for any value of $y$ , the equation has infinitely many solutions.