Question

[02.03]

Compare and Contrast: Two equations are listed below. Solve each equation and
compare the solutions. Choose the statement that is true about both solutions.
Equation 1 Equation 2
15x + 6 = 41 2x + 13 = 28
(2 points)
1) Equation 1 has more solutions than equation 2
2) Equation 1 and Equation 2 have the same number of solutions.
3) Equation 2 has more solutions than Equation 1.
4) The number of solutions cannot be determined.

Answer 1

2) Equation 1 and Equation 2 have the same number of solutions.

Explanation:

The two given equations are

1) 15x + 6 = 41 and 2) 2x + 13 = 28

Solving both equations, we get

Solving (1) : 15x + 6 = 41 ⇒ 15x = 41 - 6 = 35

or, x = 35/15 ⇒ x = 7/3

Solving (2) : 2x + 13 = 28⇒ 2x = 28 - 13 = 15

or, x = 15/2 ⇒ x = 15/2

So, from above solutions we can say that Equation 1 and Equation 2 have the same number of UNIQUE solution.