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.

Click Here to know how to solve Quadratic Equations

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 :)