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:** x^{2} + 3x – 10 = 0 and y^{2} – 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:** x^{2} – 8x + 12 = 0 and y^{2} + 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:** x^{2} + 3x – 4 = 0 and y^{2} – 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:** x^{2} – 5x + 6 = 0 and y^{2} – 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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