Question

For which value of " a" the system of equation 3x + 2y = 5 and (a + 1) x + (a - 1 ) y = 2a - 1 represents parallel lines ​

Answer 1

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Answer 2

Answer:

5

Step-by-step explanation:

Parallel lines have the same slope

Lines in slope-intercept form:

• 3x + 2y = 5 ⇒ 2y = -3x + 5 ⇒ y = -3/2 x + 5/2
• (a+1)x +(a-1)y = 2a - 1 ⇒ (a-1)y = -(a+1)x + 2a - 1 ⇒ y = -(a+1)/(a-1)x  + (2a-1)/(a-1)

So for these lines to be parallel they should have same slope.

The slope of the first line is -3/2 and of the second line is -(a+1)/(a-1)

• -(a+1)/(a-1) = -3/2
• 2(a+1) = 3(a - 1)
• 2a +2 = 3a - 3
• 3a - 2a = 2+ 3
• a = 5