Question

Which equation has infinitely many solutions?

A. -6.8 + 3y + 2.4 = 4.3 – 3y
B. 1/3y + 2.5 – 2/3y = 1.2
C. 5.1 + 2y + 1.2 = -2 + 2y +8.3
D. 2/5y = 2.3 + 3/2y

Answer 1

C. 5.1 + 2y + 1.2 = -2 + 2y + 8.3

Explanation:

-6.8 + 3y + 2.4 = 4.3 - 3y **SOLVE FOR y

-4.4 + 3y = 4.3 - 3y

3y +3y = 4.3 + 4.4

6y = 8.7

8.7 DIVIDED BY 6

y = 1.45 THEREFORE, only one solution

1/3y + 2.5 - 2/3y = 1.2 ** TRANSFORM DECIMALS TO FRACTIONS!

1/3y + 5/2 - 2/3y = 6/5 --> multiply both sides by 30

10y + 75 - 20y = 36 --> collect like terms

-10y = 36 - 75

-10y = -39

y = 3.9 or 39/10 one solution

5.1 + 2y + 1.2 = -2 + 2y + 8.3

5.1 +1.2 = -2 + 8.3 ***2y crosses out as their the same!!

6.3 = 6.3 a REAL solution; infinity many

2/5y = 2.3 + 3/2y

2/5y = 23/10 + 3/2y

4y = 23 + 15y

4y - 15y = 23

-11y = 23

y = -2.09 or -23/11 one solution

Hope I helped!!!

Answer 2

C

Explanation:

5.1 + 2y + 1.2 = -2 + 2y + 8.3 ( subtract 2y on each side)

5.1 + 1.2 = -2 + 8.3 ( collect like terms)

6.3 = 6.3

If the equation ends with a true statement (ex: 2=2) then you know that there's infinitely many solutions or all real numbers.