Question

Question: How many solutions: x + 2y = 6 and 2x − 3y = 26

Answers/Answers to choose from:
One-Solution
Infinitely Many Solutions
Or No Solution

(Basically does the question have only one solution, infinitely many solutions, or does it have no solution) Please don't guess

Answer 1

one-solution

Explanation:

(x + 2y = 6)2

2x - 3y = 26

2x + 4y = 12

2x - 3y = 26

7y = -14

y = -2

x + 2(-2) = 6

x + -4 = 6

x = 10

Answer 2

• One-Solution

Explanation:

It is two lines, if they intersect there is one solution, if parallel- no solution, if same lines- infinitely many solutions

Lets put them in slope-intercept form and compare:

• x + 2y = 6 ⇒ 2y = -x + 6 ⇒ y = -1/2x + 3
• 2x - 3y = 26 ⇒ 3y = 2x - 26 ⇒ y = 2/3x - 26/3

As we see the lines have different slopes, so they intersect which means one solution only.