### CAT Linear Equations

**Question**

**1.**x + |y| = 8, |x| + y = 6.How many pairs of x, y satisfy these two equations?

A. 2

B. 4

C. 0

D. 1

**Answer:**Choice (D)

**Explanatory Answer**

We
start with the knowledge that the modulus of a number can never be negative,
though the number itself may be negative.

The
first equation is a pair of lines defined by the equations

y
= 8 – x ------- (i) {when y is
positive}

y
= x – 8 ------- (ii) {when y is
negative}

With
the condition that x ≤ 8 (because if x becomes more
than 8, |y| will be forced to be negative, which is not allowed)

The
second equation is a pair of lines defined by the equations:

y
= 6 – x ------- (iii) {when x is
positive}

y
= 6 + x ------- (iv) {when x is
negative}

with
the condition that y cannot be greater than 6, because if y > 6, |x| will
have to be negative.

On
checking for the slopes, you will see that lines (i) and (iii) are parallel.
Also (ii) and (iv) are parallel (same slope).

Lines
(i) and (iv) will intersect, but only for x = 1; which is not possible as
equation (iv) holds good only when x is negative

Lines
(ii) and (iii) do intersect within the given constraints. We get x = 7, y = -1.
This satisfies both equations.

Only
one solution is possible for this system of equations.

Labels: CAT 2013 questions, CAT 2013 Solutions, CAT Linear Equations

## 1 Comments:

that was nice. sir, i’d like to know as to when the cat should be taken? early or late? when did you take it last year?

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