To solve Equations in Quant Section

Hello Aspirants,

In most of your exams, 5 questions come from the topic Equations (Linear, Quadratic). In these questions you are given 2 equations in 2 variables. You have to solve these equations to find the value/s of these 2 variables and tell that what is the relation between these 2 variables.

You can answer these questions by plotting the values on number line. You don’t have to remember any rule for these questions.

Here I am giving you some examples of quadratic equations.

Ex 1: x2 + 3x – 10 = 0 and y2 – 7y + 12 = 0

By solving we get x = -5, 2 and y = 3, 4
Put these values as on a number line as:
-5(x)           2(x)     3(y)      4(y)
By this, it is clear that x is always less than y. So, we will say x < y.

Ex 2: x2 – 8x + 12 = 0 and y2 + 3y – 10 = 0

By solving we get x = 2, 6 and y = -5, 2
Put these values as on a number line as:
-5(y)             2(y,x)         6(x)
When x = 2, x = y=2 and x > y = -5, so x ≥ y.
When x = 6, x > y = 2 and x > y = -5.
By this, it is clear that either x is greater than y always or is equal to y at value 2. So, we will say x ≥ y.

Ex 3: x2 + 3x – 4 = 0 and y2 – y – 6 = 0

By solving we get x = -4, 1 and y = -2, 3
Put these values as on a number line as:
-4(x)             -2(y)         1(x)       3(y)
When there are values in between, one cannot find the relationship. So, we will say that no relationship exists between x and y.

Ex 4: x2 – 5x + 6 = 0 and y2 – 7y + 10 = 0

By solving we get x = 2, 3 and y = 2, 5
Put these values as on a number line as:
2(x,y)        3(x)            5(y)
When x = 2, x = y=2 and x < y = 5, so x ≤ y.
When x = 3, x > y = 2 and x < y = 5.
By these values, one cannot find the exact relationship. So, we will say that no relationship exists between x and y.

Happy learning :)

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